- Partial Differential Equations Department

Head / Chief Researcher **Office**: room 209, University str.11, 0186 Tbilisi, Georgia**Phone**: 593316280**E-mail**: tjangv@yahoo.com**Research fields**: Differential and Integro-Differential Equations; Numerical Analysis; Nonlocal Problems

After graduating from the Faculty of Cybernetics and Applied Mathematics of the I.Javakhishvili Tbilisi State University (TSU) in 1977, I started working at the I. Vekua Institute of Applied Mathematics of TSU, where today I am the chief researcher and head of the Department of Partial Differential Equations. Since 1977 I was working in different positions at TSU beginning from assistant professor to full professor. From 1980 to1983, I was a post-graduate student at TSU under the supervision of academician Andro Bitsadze, and I often had to visit the V.A.Steklov Mathematical Institute and the M.V.Lomonosov Moscow State University. I defended dissertations for Candidate of Science in 1984 and Doctor of Science in 1998. Since 1977 I have been giving lectures on various fields of mathematics at TSU, Georgian Technical University (GTU), Sokhumi State University, Ilia State University and Caucasian University. Since 2013 I am a professor at the GTU. From 2012 to 2013, I was a visiting professor at the Naval Postgraduate School in California under Fulbright grant program. One of the main results of this grant program was the publication of the following monograph Jangveladze T., Kiguradze Z., Neta B. Numerical Solution of Three Classes of Nonlinear Parabolic Integro-Differential Equations. Elsevier, 2016, ACADEMIC PRESS, ISBN: 978-0-12-804628-9. Elsevier/Academic Press, Amsterdam, 2015. 254 p. I am the Principal Investigator and main executor of various international and national scientific and educational grants. I participated in many international conferences, was a member and co-chair of the organizing and scientific committees. I am the chairman of the National Committee of the Georgian Mathematical Union; Academician of the Tskhum-Abkhazian Academy of Sciences; referee for peer-reviewed journals Mathematical Reviews and Zentralblatt fur Mathematik; Member of the editorial board of several top scientific journals and editor of one of them. In 2016 I was awarded by the Georgian National Academy of Sciences a Certificate of Honor in connection with the World Science Day established by UNESCO, for scientific achievements in the field of Mathematics. I am the author or co-author of more than 200 publications, including 3 monographs and 10 textbooks. My scientific interests are: differential and integro-differential equations and systems; nonlinear models of mathematical physics; numerical analysis; non-local problems. Under my supervision, 11 doctoral and 45 master's theses were defended. Many of the authors work in scientific or educational institutions in Georgia and abroad. Many bachelor's theses and grant projects have also been prepared. In particular, under my leadership, the following scholarships were awarded to young scientist: Presidential Grant of the Shota Rustaveli National Science Foundation for a young scientists PG/86/5-106/12, 2012 (Mikheil Gagoshidze); Joint program of the US Civilian Research and Development Foundation (CRDF-Global), Shota Rustaveli National Science Foundation and the Science and Technology Development Foundation of Georgia "Scientific Research Grant program for Georgian Women", 2014 (Maya Nikolishvili); Doctoral programs of the Shota Rustaveli National Science Foundation: DO/361/5-106/14, 2015 (Maya Aptsiauri); PhDF2016-19, 2016 (Maya Kratsashvili); PhDF2016-14, 2016 (Besiki Tabatadze); Keele University, UK. Erasmus+ Exchange Program, 2019 (George Tsulaya).

- Investigation and Approximate Solution of Some Nonlinear Partial Differential and Integro-Differential Models (FR-21-2101), 2022-2025.
- On Investigation and Approximate Solution of Two Nonlinear Diffusion Models (Travel Grant, Turkey) (MG_101), 2017-2017.
- Investigation and Numerical Solution of Some Nonlinear Integro-Differential Models Based on Maxwell System (CNRS/SRNSF 2013, 04/26), 2014-2016.
- Large Time Behavior and Semi-Discrete Scheme for One Nonlinear Partial Integro-Differential Equation (Florida, USA) (2014_tr_405), 2014-2014.
- Investigation and Numerical Solution of Some Nonlinear Nonstationary Models (FR/30/5-101/12), 2013-2016.
- Investigation and numerical resolution of some nonlinear diffusion systems (AY 2012-2013), 2012-2013.
- Constraint Logic Programming over Unranked Terms and Hedges with Description Operators (13-08), 2012-2015.
- Investigation and Numerical Solution of Some Classes of Nonlinear Partial Differential and Integro-differential Equations (GNSF/ST07/3-176), 2008-2010.

*On Two Multidimensional Systems of Nonlinear Partial Differential Equations*, by**Temur Jangveladze (Speaker)**at XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), Tbilisi, Georgia, 22-24 April, 2024.*Numerical Solution of Two Systems of Nonlinear Partial Differential Equations Using Machine Learning*, by**Mikheil Gagoshidze (Speaker), Temur Jangveladze, Zurab Kiguradze**at 7th International Conference on Advances in Natural and Applied Sciences (ICANAS 2024), Antalya, Turkey, 17-20 April, 2024.*Numerical Solution of One Nonlinear Fourth-Order Integro-Differential Parabolic Equation Using Machine Learning*, by**Besiki Tabatadze (Speaker), Teimuraz Chkhikvadze, Temur Jangveladze, Zurab Kiguradze**at 7th International Conference on Advances in Natural and Applied Sciences (ICANAS 2024), Antalya, Turkey, 17-21 April, 2024.*On Decomposition Method for Bitsadze-Samarskii Nonlocal Boundary Value Problem for Nonlinear Two-Dimensional Second Order Elliptic Equations*, by**Temur Jangveladze (Speaker)**at International Workshop on the Qualitative Theory of Differential Equations, QUALITDE–2023, Tbilisi, Georgia, 09-11 December, 2023.*Two Methods of the Numerical Solution of One System of Nonlinear Partial Differential Equations*, by**Besiki Tabatadze (Speaker), Mikheil Gagoshidze , Temur Jangveladze, Zurab Kiguradze**at Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS" Dedicated to the 105th Anniversary of I.Javakhishvili Tbilisi State University (TSU) & 55th Anniversary of I.Vekua Institute of, Tbilisi, Georgia, 13-15 September, 2023.*Some Properties and Numerical Solution of Initial-Boundary Value Problem for One System of Nonlinear Partial Differential Equations*, by**Mikheil Gagoshidze (Speaker), Temur Jangveladze, Zurab Kiguradze**at XIII International Conference of the Georgian Mathematical Union,, Batumi, Georgia, 04-09 September, 2023.*Numerical Solution of One Two-Dimensional System of Nonlinear Partial Differential Equations*, by**Besiki Tabatadze (Speaker), Mikheil Gagoshidze , Temur Jangveladze, Zurab Kiguradze**at XIII International Conference of the Georgian Mathematical Union, Batumi, Georgia, 04-09 September, 2023.*On One Nonlinear Parabolic Integro-Differential Model*, by**Teimuraz Chkhikvadze (Speaker), Mikheil Gagoshidze , Temur Jangveladze, Zurab Kiguradze**at XIII International Conference of the Georgian Mathematical Union, Batumi, Georgia, 04-09 September, 2023.*Comparative Analysis of Approximate Solutions for a Numerical Solution of a Two-Dimensional Nonlinear Model.*, by**Besiki Tabatadze (Speaker), Temur Jangveladze, Mikheil Gagoshidze**at The Tbilisi Analysis & PDE Workshop (TAPDE Workshop 2023), Tbilisi, Georgia, from 30 August to 02 September, 2023.*On two systems of nonlinear partial differential equations*, by**Mikheil Gagoshidze (Speaker), Temur Jangveladze, Zurab Kiguradze**at Third International Conference MATHEMATICS IN ARMENIA Advances and Perspectives, Dedicated to the 80th anniversary of foundation of Armenian National Academy of Sciences, Yerevan, Armenia, 02-08 July, 2023.*On one nonlinear fourth-order integro-differential parabolic equation*, by**Besiki Tabatadze (Speaker), Teimuraz Chkhikvadze, Temur Jangveladze, Zurab Kiguradze**at Third International Conference MATHEMATICS IN ARMENIA: Advances and Perspectives. Dedicated to the 80th anniversary of foundation of Armenian National Academy of Sciences, Yerevan, Armenia, 02-08 July, 2023.*On the system of Maxwell's nonlinear partial differential equations*, by**Temur Jangveladze (Speaker)**at XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), Tbilisi, Georgia, 19-22 April, 2023.*On Investigation and Numerical Solution of One Nonlinear Fourth-Order Integro-Differential Model*, by**Tamar Faiqidze (Speaker), Teimuraz Chkhikvadze, Temur Jangveladze**at XII International Conference of the Georgian Mathematical Union, Batumi, Georgia, from 29 August to 03 September, 2022.*Asymptotic Properties and Approximate Solution of Initial-Boundary Value Problem for One Nonlinear Partial Differential Model*, by**Nino Mzhavanadze (Speaker), Mikheil Gagoshidze , Temur Jangveladze**at XII International Conference of the Georgian Mathematical Union, Batumi, Georgia, from 29 August to 03 September, 2022.*Investigation and Approximate Solution of Nonlinear One-Dimensional Maxwell System*, by**Mikheil Gagoshidze (Speaker), Temur Jangveladze, Zurab Kiguradze**at XIII Annual International Meeting of the Georgian Mechanical Union, Batumi, Georgia, 24-26 August, 2022.*On investigation and approximate solution of two systems of nonlinear partial differential equations*, by**Temur Jangveladze (Speaker)**at XXXVI International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), Tbilisi, Georgia, 19-21 April, 2022.*Hopf Bifurcation and its Computer Simulation for One-Dimensional Maxwell's Model*, by**Temur Jangveladze (Speaker), Mikheil Gagoshidze**at XXX Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU)., Tbilisi, Georgia, 20-22 April, 2022.*On One System of Nonlinear Degenerate Integro-Differential Equations of Parabolic Type. International Workshop on the Qualitative Theory of Differential Equations*, by**Temur Jangveladze (Speaker)**at International Workshop on the Qualitative Theory of Differential Equations, QUALITDE-2021, Dedicated to the 130th birthday anniversary of Academician N. Muskhelishvili, Tbilisi, Georgia, 18-20 December, 2021.*On Investigation and Approximate Solution of Nonlinear Model Describing Electromagnetic Field Diffusion Process*, by**Temur Jangveladze (Speaker)**at XI Internatnal Conference of the Georgian Mathematical Union, Batumi, Georgia, 23-28 August, 2021.*On the Problem with Nonlocal Boundary Conditions for One Nonlinear Integro-Differential Equation*, by**Temur Jangveladze (Speaker)**at XXXV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), Tbilisi, Georgia, 21-24 April, 2021.*On One Nonlinear Degenerate Integro-Differential Equation of Parabolic Type*, by**Temur Jangveladze (Speaker)**at International Workshop on the Qualitative Theory of Differential Equations, QUALITDE–2020, Tbilisi, Georgia, 19-21 December, 2020.*Investigation and Approximate Solution of Nonlinear Integro-Differential Equation of Diffusion Type*, by**Temur Jangveladze (Speaker)**at XXXIV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), Tbilisi, Georgia, 22-24 April, 2020.*On Investigation and Approximate Solution of One System of Nonlinear Two-Dimensional Partial Differential Equations*, by**Temur Jangveladze (Speaker)**at International Workshop on the Qualitative Theory of Differential Equations, QUALITDE-2019, Tbilisi, Georgia, 07-09 December, 2019.*On a Numerical Solution of One Two-Dimensional Nonlinear Model*, by**Besiki Tabatadze (Speaker), Temur Jangveladze**at The Fourth International Conference on Applications of Mathematics and Informatics in Natural Sciences and Engineering. AMINSE 2019, Tbilisi, Georgia, 23-26 September, 2019.*On a Nonlinear Integro-Differential Equation of Parabolic Type*, by**Temur Jangveladze (Speaker)**at XXXIII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), Tbilisi, Georgia, 23-25 April, 2019.*On Additive Averaged Semi-Discrete Scheme for One Nonlinear Multi-Dimensional Integro-Differential Equation. International Workshop on the Qualitative Theory of Differential Equations*, by**Temur Jangveladze (Speaker)**at International Workshop on the Qualitative Theory of Differential Equations, QUALITDE-2018, Dedicated to the 100th Anniversary of I. Javakhishvili Tbilisi State University, Tbilisi, Georgia, 01-03 December, 2018.*Correctness and Additive Averaged Semi-Discrete Scheme for Two Nonlinear Multi-Dimensional Integro-Differential Parabolic Problems*, by**Temur Jangveladze (Speaker)**at International Workshop on the Qualitative Theory of Differential Equations – QUALITDE-2017, Tbilisi, Georgia, 24-26 December, 2017.*Asymptotic Properties of Solution and Difference Scheme for One Nonlinear Integro-Differential Model*, by**Zurab Kiguradze (Speaker), Temur Jangveladze**at The Third International Conference on Applications of Mathematics and Informatics in Natural Sciences and Engineering Dedicated to the 80th Birthday of David Gordeziani AMINSE 2017, Tbilisi, Georgia, 06-09 December, 2017.*On Investigation and Approximate Solution of Two Nonlinear Diffusion Models*, by**Temur Jangveladze (Speaker)**at 4th International Conference on Pure and Applied Sciences (Renewable Energy), ICPAS 2017, Istanbul, Turkey, 23-25 November, 2017.*Convergence Analysis for Finite Difference Scheme of One Nonlinear Integro-Differential Model with Source Term*, by**Maia Kratsashvili (Speaker), Temur Chilachava, Temur Jangveladze**at 4th International Conference on Pure and Applied Sciences (Renewable Energy), ICPAS 2017, Istanbul, Turkey, 23-25 November, 2017.*Investigation and Approximate Solution of Two Systems of Nonlinear Partial Differential Equations*, by**Temur Jangveladze (Speaker)**at The 2017 International Conference on Pure Mathematics - Applied Mathematics (PM-AM 2017), Plenary Lecture, Athens, Greece, 09-11 April, 2017.*Unique Solvability and Additive Averaged Rothe's Type Scheme for One Nonlinear Multi-Dimensional Integro-Differential Parabolic Problem*, by**Temur Jangveladze (Speaker)**at International Workshop on the Qualitative Theory of Differential Equations – QUALITDE-2016, Tbilisi, Georgia, 24-26 December, 2016.*Hopf Bifurcation and its Computer Simulation for One-Dimensional Maxwell's Model*, by**Temur Jangveladze (Speaker), Mikheil Gagoshidze**at XXX Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), Tbilisi, Georgia, 20-22 April, 2016.*Investigation and Approximate Resolution of One Nonlinear Integro-Differential Parabolic Equation*, by**Temur Jangveladze (Speaker)**at International Workshop on the Qualitative Theory of Differential Equations, QUALITDE – 2015, Tbilisi, Georgia, 27-29 December, 2015.*On Two Nonlinear Partial Integro-Differential Models*, by**Temur Jangveladze (Speaker)**at 4th International Conference on Applied and Computational Mathematics (ICACM’15). Plenary Lecture, Seoul, Korea, 05-07 September, 2015.*Investigation and Numerical Resolution of Two Types Nonlinear Partial Integro-Differential Models*, by**Temur Jangveladze (Speaker)**at VI Annual International Conference of the Georgian Mathematical Union, Batumi, Georgia, 12-26 July, 2015.*On One System of Nonlinear Multi-dimensional Partial Differential Equations*, by**Temur Jangveladze (Speaker), Zurab Kiguradze**at SIAM SEAS Conference, Alabama, USA, 20-22 March, 2015.*One Nonlinear Model Based on Maxwell System*, by**Zurab Kiguradze (Speaker), Temur Jangveladze**at SIAM SEAS Conference, Alabama, USA, 20-22 March, 2015.*Some Properties of Solutions and Approximate Algorithms for One System of Nonlinear Partial Differential Equations*, by**Temur Jangveladze (Speaker)**at International Workshop on the Qualitative Theory of Differential Equations, QUALITDE – 2014, Dedicated to the 125th birthday anniversary of Professor A. Razmadze, Tbilisi, Georgia, 18-20 December, 2014.*On Investigation and Approximate Solution of One Nonlinear Partial Integro-Differential Equation with Source Term*, by**Zurab Kiguradze (Speaker), Temur Jangveladze**at Proceedings of the 8th International Conference on Applied Mathematics, Simulation, Modelling (ASM '14), Florence, Italy, 22-24 November, 2014.*On Numerical Solution of One Nonlinear Multi-Dimensional System of Partial Differential Equations*, by**Temur Jangveladze (Speaker), Mikheil Gagoshidze**at V Annual Conference of Georgian Mathematical Union, Batumi, Georgia, 08-12 September, 2014.*Finite Difference and Finite Element Approximations for One Nonlinear Partial Integro-Differential Equation*, by**Temur Jangveladze (Speaker)**at 7th International Conference on Finite Differences, Finite Elements, Finite Volumes, Boundary Elements, Gdansk, Poland, 15-17 May, 2014.*Large Time Behavior and SemiDiscrete Scheme for One Nonlinear Partial Integro-Differential Equation*, by**Temur Jangveladze (Speaker), Zurab Kiguradze, Mikheil Gagoshidze**at SIAM SEAS Conference, Florida Institute of Technology Melbourne, USA, Florida, March 29-30, 2014. SIAM Abstracts Book, 2014, p.47., Florida, USA, 29-30 March, 2014.*On Some Properties and Approximate Solution of One System of Nonlinear Partial Differential Equations*, by**Temur Jangveladze (Speaker)**at International Workshop on the Qualitative Theory of Differential Equations, QUALITDE – 2013, Dedicated to the 100th birthday anniversary of Professor Levan Magnaradze, Tbilisi, Georgia, 20-22 December, 2013.*Variable Directions Difference Scheme for One System of Nonlinear Partial Differential Equations*, by**Temur Jangveladze (Speaker)**at 2nd international conference on applied, numerical and computational mathematics, Morioka City, Iwate, Japan, 23-25 April, 2013.*Investigation and Numerical Resolution of Some Nonlinear Partial Differential and Integro-Differential Models*, by**Temur Jangveladze (Speaker)**at 5th WSEAS International Conference on FINITE DIFFERENCES - FINITE ELEMENTS - FINITE VOLUMES - BOUNDARY ELEMENTS (F-and-B '12), Prague, Czech Republic, 24-26 September, 2012.*On One Nonlinear Diffusion System*, by**Mikheil Gagoshidze (Speaker), Temur Jangveladze**at XXV Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia, 20-23 April, 2011.*Investigation and Numerical Solution of System of Nonlinear Integro-Differential Equations Associated with the Penetration of a Magnetic Field in a Substance*, by**Temur Jangveladze (Speaker)**at MATH'10: Proceedings of the 15th WSEAS international conference on Applied mathematics, Athens, Greece, 29-31 December, 2010.

**Temur Jangveladze, Zurab Kiguradze, Teimuraz Chkhikvadze**,*Application of Deep Neural Network for Numerical Approximation for Averaged Nonlinear Integro-Differential Equation*, Bulletin of TICMI, V.28 (accepted), Tbilisi University Press, 2024.**Temur Jangveladze, Mikheil Gagoshidze , Zurab Kiguradze, Besiki Tabatadze**,*Tabatadze B.Two Methods of the Numerical Solution of One System of Nonlinear Partial Differential Equations*, Lecture Notes of TICMI, V.25, (accepted), Tbilisi University Press, 2024.**Temur Jangveladze**,*On the System of Maxwell's Nonlinear Partial Differential Equations*, Rep. Enlarged Sess. Semin. I.Vekua Inst. Appl. Math.,V.37, 15-18., Tbilisi University Press, 2023.**Temur Jangveladze**,*On Decomposition Method for Bitsadze-Samarskii Nonlocal Boundary Value Problem for Nonlinear Two-Dimensional Second Order Elliptic Equations*, International Workshop on the Qualitative Theory of Differential Equations, QUALITDE–2023, REPORTS OF QUALITDE, V.2, p.66-70, Tbilisi State University Press, 2023.**Temur Jangveladze, Zurab Kiguradze, Maia Kratsashvili, Beny Neta**,*Numerical solution for a nonlinear diffusion model with source terms*, Georgian Mathematical Journal, V.30, N4, 539-554. , Georgian Mathematical Journal, 2023.**Temur Jangveladze**,*Finite Difference Scheme for One System of Nonlinear Partial Differential Equations*, Bulletin of the Georgian National Academy of Sciences, V.16, N2, p.16-22 , Georgian National Academy of Sciences, 2022.**Temur Jangveladze**,*Some Properties of the Initial-Boundary Value Problem for One System of Nonlinear Partial Differential Equations*, Bulletin of TICMI, V.25, N2, p.137-143, Tbilisi University Press, 2021.**Temur Jangveladze, Mikheil Gagoshidze**,*An Analysis of the Hopf Bifurcation and Computer Simulation for One-Dimensional Maxwell-Type Nonlinear System*, Tskhum-Abkhazian Academy of Sciences, Proceedings, V.XXI, 186-200, Meridiani, 2021.**Temur Jangveladze**,*On One System of Nonlinear Degenerate Integro-Differential Equations of Parabolic Type*, International Workshop on the Qualitative Theory of Differential Equations, QUALITDE-2021, Dedicated to the 130th birthday anniversary of Academician N. Muskhelishvili, p.78–82, Tbilisi University Press, 2021.**Temur Jangveladze, Zurab Kiguradze**,*Unique Solvability and Decomposition Method for One Nonlinear Multi-Dimensional Integro-Differential Parabolic Equation*, International Journal of Numerical Analysis and Modeling, V.17, N6, p.806-819, University of Alberta, 2020.**Temur Jangveladze, Zurab Kiguradze**,*Averaged Semi-Discrete Scheme of Sum-Approximation for One Nonlinear Multi-Dimensional Integro-Differential Parabolic Equation*, Georgian Mathematical Journal, V.27, N3, p.367-373, De Gruyter, 2020.**Temur Jangveladze**,*On One Nonlinear Degenerate Integro-Differential Equation of Parabolic Type*, International Workshop on the Qualitative Theory of Differential Equations, QUALITDE–2020, p.95–98., Tbilisi University Press, 2020.**Temur Jangveladze**,*Investigation and approximate solution of nonlinear integro-differential equation of diffusion type*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Vol. 34, 38-41, Tbilisi University Press, 2020.**Temur Jangveladze**,*On One Nonlinear Integro-Differential Equation*, Tskhum-Abkhazian Academy of Sciences, Proceedings, V. XIX – XX, p.230–239, Meridiani, 2020.**Temur Jangveladze, Zurab Kiguradze, Mikheil Gagoshidze**,*Economical Difference Scheme for One Multi-Dimensional Nonlinear System*, Acta Mathematica Scientia, Vol. 39 (4), 971-988, Springer, 2019.**Temur Jangveladze, Zurab Kiguradze**,*Asymptotic Properties of Solution and Difference Scheme for One Nonlinear Integro-Differential Model*, AMINSE 2017: Mathematics, Informatics, and Their Applications in Natural Sciences and Engineering, pp. 117–133, Springer, 2019.**Temur Jangveladze**,*On Investigation and Approximate Solution of One System of Nonlinear Two-Dimensional Partial Differential Equations*, International Workshop on the Qualitative Theory of Differential Equations, QUALITDE-2019, Tbilisi University Press, 2019.**Temur Jangveladze**,*Investigation and Numerical Solution of Nonlinear Partial Differential and Integro-Differential Models Based on System of Maxwell Equations*, Memoirs on Differential Equations and Mathematical Physics, V.76, p.1-118, Andrea Razmadze Mathematical Institute, 2019.**Frédéric Hecht, Temur Jangveladze, Zurab Kiguradze, Olivier Pironneau**,*Finite Difference Scheme for One System of Nonlinear Partial Integro-Differential Equations*, Applied Mathematics and Computation, V.328, p.287-300, Elsevier, 2018.**Temur Jangveladze, Zurab Kiguradze, Maia Kratsashvili**,*Uniqueness of Solution and Fully Discrete Scheme to Nonlinear Integro-Differential Averaged Model with Source Terms*, Miskolc Mathematical Notes, V.19, N2, p.907-921, Miskolc University Press, 2018.**Temur Jangveladze**,*On Additive Averaged Semi-Discrete Scheme for One Nonlinear Multi-Dimensional Integro-Differential Equation. International Workshop on the Qualitative Theory of Differential Equations*, International Workshop on the Qualitative Theory of Differential Equations, QUALITDE-2018, Dedicated to the 100th Anniversary of I. Javakhishvili Tbilisi State University, Tbilisi University Press, 2018.**Frédéric Hecht, Temur Jangveladze, Zurab Kiguradze, Olivier Pironneau**,*Finite difference Scheme for One System of Nonlinear Partial Integro-Differential equations*, Applied Mathematics and Computation, Elsevier, 2018.**Temur Jangveladze, Maia Kratsashvili**,*Some Properties of Solution and Finite Difference Scheme for One Nonlinear Partial Differential Model Based on Maxwell System*, Memoirs on Differential Equations and Mathematical Physics, V.73, p.83-92, Andrea Razmadze Mathematical Institute, 2018.**Temur Jangveladze, Zurab Kiguradze, Mikheil Gagoshidze , Besiki Tabatadze**,*Comparison of Two Methods of Numerical Solution of Mitchison Biological System of Nonlinear Partial Differential Equations*, International Journal of Mathematics and Computers in Simulation, V.11, p.25-31, Elsevier, 2017.**Temur Jangveladze, Zurab Kiguradze**,*Investigation and Rothe’s Type Scheme for Nonlinear Integro-Differential Multi-Dimensional Equations Associated with the Penetration of a Magnetic Field in a Substance*, International Journal of Mathematical Models and Methods in Applied Sciences, V.11, p.75-81, World Scientific, 2017.**Temur Jangveladze, Zurab Kiguradze, Maia Kratsashvili**,*Correctness of the Initial-Boundary Value Problem and Discrete Analogs for One Nonlinear Parabolic Integro-Differential Equation*, International Journal of Pure Mathematics, V.4, p.7-11, SciPress Ltd, 2017.**Temur Jangveladze**,*Investigation and Approximate Solution of Two Systems of Nonlinear Partial Differential Equations*, International Journal of Pure Mathematics, V.4, p.1-6, SciPress Ltd, 2017.**Temur Jangveladze**,*Correctness and Additive Averaged Semi-Discrete Scheme for Two Nonlinear Multi-Dimensional Integro-Differential Parabolic Problems*, International Workshop on the Qualitative Theory of Differential Equations – QUALITDE-2017, p.67–70, Georgian Technical University Press, 2017.**Temur Jangveladze**,*Well-posedness and approximate solution of the initial-boundary value problem for nonlinear integro-differential equation obtained by the reduction of Maxwell system*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Vol. 31, 59-62, Tbilisi University Press, 2017.**Temur Jangveladze**,*Long-Time Behavior of Solution and Semi-Discrete Scheme for One Nonlinear Parabolic Integro-Differential Equation*, Transactions of A.Razmadze Mathematical Institute, V.170, N1, p.47-55, Elsevier BV, 2016.**Temur Jangveladze, Zurab Kiguradze**,*Finite Difference Scheme for One Nonlinear Parabolic Integro-Differential Equation*, Transactions of A.Razmadze Mathematical Institute, V.170, N3, p.395-401, Elsevier BV, 2016.**Temur Jangveladze, Mikheil Gagoshidze**,*Hopf Bifurcation and its Computer Simulation for One-Dimensional Maxwell's Model*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Vol. 30, 27-30, Tbilisi University Press, 2016.**Temur Jangveladze, Zurab Kiguradze**,*Difference Scheme for One System of Nonlinear Parabolic Integro-Differential Equations*, Applied Mathematics, Informatics, and Mechanics, V.21, N1, p.104-120, Tbilisi University Press, 2016.**Temur Jangveladze**,*Unique Solvability and Additive Averaged Rothe's Type Scheme for One Nonlinear Multi-Dimensional Integro-Differential Parabolic Problem*, International Workshop on the Qualitative Theory of Differential Equations – QUALITDE-2016, p.103-106, Georgian Technical University Press, 2016.**Mikheil Gagoshidze , Temur Jangveladze, Zurab Kiguradze, Maia Nikolishvili**,*Stability and Convergence of the Variable Directions Difference Scheme for One Nonlinear Two-dimensional Model*, International Journal of Biomathematics, V.8, N5, 1550057 (21 pages), World Scientific, 2015.**Temur Jangveladze**,*On Two Classes of Nonlinear Partial Differential Systems*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, V.29, p.52-55, Tbilisi University Press, 2015.**Temur Jangveladze, Zurab Kiguradze, Beny Neta**,*Numerical Solution of Three Classes of Nonlinear Parabolic Integro-Differential Equations*, Amsterdam, 254 p., Elsevier/Academic Press, 2015.**Temur Jangveladze**,*Investigation and Approximate Resolution of One Nonlinear Integro-Differential Parabolic Equation*, International Workshop on the Qualitative Theory of Differential Equations, QUALITDE – 2015, p.64-67, Tbilisi University Press, 2015.**Temur Jangveladze, Zurab Kiguradze, Giorgi Lobjanidze**,*Variational Statement and Domain Decomposition Algorithms for Bitsadze-Samarskii Nonlocal Boundary Value Problem for Poisson’s Two-Dimensional Equation*, International Journal of Partial Differential Equations, Volume 2014, Article ID 680760, 8 pages, Hindawi Publishing Corporation, 2014.**Temur Jangveladze, Maia Kratsashvili**,*Asymptotic Behavior of Solution and Semi-Discrete Difference Scheme for One Nonlinear Integro-Differential Equation with Source Term*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, V.28, p.50-53, Tbilisi University Press, 2014.**Temur Jangveladze, Zurab Kiguradze, Mikheil Gagoshidze**,*Large Time Behavior of Solution and Semi-Discrete Scheme for One Nonlinear Integro-Differential Equation with Source Terms*, Journal of Applied Mathematics and Mechanics, V.19, N2, p.10-17, Elsevier, 2014.**Temur Jangveladze**,*Some Properties and Numerical Solution of One-Dimensional Nonlinear Electromagnetic Diffusion System. Advances in Applied and Pure Mathematics*, Proceedings 7th International Conference on Finite Differences, Finite Elements, Finite Volumes, Boundary Elements, p.96-100, Elsevier, 2014.**Temur Jangveladze**,*Some Properties of Solutions and Approximate Algorithms for One System of Nonlinear Partial Differential Equations*, International Workshop on the Qualitative Theory of Differential Equations, QUALITDE – 2014, Dedicated to the 125th birthday anniversary of Professor A. Razmadze, p.54-57, Tbilisi University Press, 2014.**Temur Jangveladze, Zurab Kiguradze**,*On Investigation and Approximate Solution of One Nonlinear Partial Integro-Differential Equation with Source Term*, Recent Advances in Applied Mathematics, Modelling and Simulation. Proceedings of the 8th International Conference on Applied Mathematics, Simulation, Modelling (ASM '14), p.50-55, WSEAS Press, 2014.**Temur Jangveladze, Zurab Kiguradze**,*Semi-discrete Scheme for One Nonlinear Integro-Differential System Describing Diffusion Process of Electromagnetic Field*, Advances in Applied and Pure Mathematics, Advances in Applied and Pure Mathematics, 2014.**Temur Jangveladze, Zurab Kiguradze, Giorgi Lobjanidze**,*On Variational Formulation and Domain Decomposition Method for Bitsadze-Samarskii Nonlocal Boundary Value Problem*, Recent Advances in Mathematical Methods and Computational Techniques in Modern Science, p.130-134, Springer, 2013.**Temur Jangveladze, Zurab Kiguradze**,*On Some Nonlinear Partial Differential and Integro-Differential Diffusion Models*, Recent Advances in Mathematical Methods and Computational Techniques in Modern Science, p.124-129, Springer, 2013.**Temur Jangveladze**,*Variable Directions Difference Scheme for One System of Nonlinear Partial Differential Equations*, Recent Advances in Mathematical Methods and Computational Techniques in Modern Science, p.119-123, Springer, 2013.**Temur Jangveladze, Zurab Kiguradze, Maia Kratsashvili**,*Asymptotic Behavior of the Solution and Semi-Discrete Finite Difference Scheme for One Nonlinear Integro-Differential Model with Source Terms*, Applied Mathematics, Informatics, and Mechanics, V.18, N2, p.19-30, Tbilisi University Press, 2013.**Temur Jangveladze, Zurab Kiguradze, Beny Neta, Simeon Reich**,*Finite Element Approximations of a Nonlinear Diffusion Model with Memory*, Numerical Algorithms, V.64, N1, p.127-155, Springer, 2013.**Temur Jangveladze**,*On Some Properties and Approximate Solution of One System of Nonlinear Partial Differential Equations*, International Workshop on the Qualitative Theory of Differential Equations, QUALITDE – 2013, Dedicated to the 100th birthday anniversary of Professor Levan Magnaradze, p.58-60, Tbilisi University Press, 2013.**Temur Jangveladze**,*On Some Nonlinear Partial Differential and Integro-Differential Diffusion Models*, Recent Advances in Mathematical Methods and Computational Techniques in Modern Science. Proc. 2nd International Conference on Applied, Numerical and Computational Mathematics, p.124-129, WSEAS Press, 2013.**Temur Jangveladze, Zurab Kiguradze**,*On one nonlinear integro-differential equation with source term*, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, Vol. 27, 23-26, Tbilisi University Press, 2013.**Temur Jangveladze, Zurab Kiguradze, Beny Neta**,*Finite Element Method for a System of Nonlinear Integro-differential Equations with Mixed Boundary Conditions*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, V.26, p.23-28, Tbilisi University Press, 2012.**Maia Aptsiauri, Temur Jangveladze, Zurab Kiguradze**,*Asymptotic Behavior of the Solution of a System of Nonlinear Integro-Differential Equations*, Differential Equations, V.48, N1, p.72-80., Springer, 2012.**Temur Jangveladze, Zurab Kiguradze**,*Large Time Behavior of the Solution to an Initial-Boundary Value Problem with Mixed Boundary Conditions for a Nonlinear Integro-Differential Equation*, Central European Journal of Mathematics, V.9, N4, p.866-873, Walter de Gruyter, 2011.**Mikheil Gagoshidze , Temur Jangveladze**,*On One Nonlinear Diffusion System*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Vol. 25, 39-43, Tbilisi University Press, 2011.**Temur Jangveladze, Zurab Kiguradze, Beny Neta**,*Galerkin Finite Element Method for One Nonlinear Integro-Differential Model*, Applied Mathematics and Computation, V.217, N16, p.6883-6892, Elsevier, 2011.**Temur Jangveladze, Giorgi Lobjanidze**,*On One Nonlocal Boundary Value Problem for a Fourth-Order Ordinary Differential Equation*, Differential Equations, V.47, N2, p.179-186, Springer, 2011.**Temur Jangveladze, Zurab Kiguradze**,*Asymptotics for Large Time of Solutions to Nonlinear System Associated with the Penetration of a Magnetic Field into a Substance*, Applications of Mathematics, V.55, N6, p.471-493, Springer, 2010.**Temur Jangveladze, Zurab Kiguradze, Beny Neta**,*Large Time Asymptotic and Numerical Solution of a Nonlinear Diffusion Model with Memory*, Computers & Mathematics with Applications, V.59, N1, p.254-273, Elsevier, 2010.**Temur Jangveladze**,*Investigation and Numerical Solution of System of Nonlinear Integro-Differential Equations Associated with the Penetration of a Magnetic Field in a Substance*, RECENT RESEARCHES in APPLIED. MATHEMATICS. 15th WSEAS International Conference on APPLIED. MATHEMATICS (MATH '10), p.79-84, World Scientific and Engineering Academy and Society, 2010.**Temur Jangveladze, Maia Nikolishvili, Besiki Tabatadze**,*On One Nonlinear Two-Dimensional Diffusion System*, RECENT RESEARCHES in APPLIED. MATHEMATICS. 15th WSEAS International Conference on APPLIED. MATHEMATICS (MATH '10), p. 105-108, World Scientific and Engineering Academy and Society, 2010.**Temur Jangveladze, Zurab Kiguradze, Giorgi Lobjanidze**,*On Decomposition Methods and Variational Formulation for Bitsadze-Samarskii Nonlocal Boundary Value Problem for Two-Dimensional Second Order Elliptic Equations*, RECENT RESEARCHES in APPLIED. MATHEMATICS. 15th WSEAS International Conference on APPLIED. MATHEMATICS (MATH '10), p.116-121, World Scientific and Engineering Academy and Society, 2010.**Temur Jangveladze**,*Additive models for one nonlinear diffusion system*, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, Vol. 24, 66-69, Tbilisi University Press, 2010.**Temur Jangveladze, Giorgi Lobjanidze**,*Variational formulation of one nonlocal boundary problem*, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, Vol. 23, 46-49, Tbilisi University Press, 2009.**Temur Jangveladze, Zurab Kiguradze**,*Asymptotics of Solution and Finite Difference Scheme to a Nonlinear Integro-Differential Equation Associated with the Penetration of a Magnetic Field into a Substance*, WSEAS Transactions on Mathematics, V.8, N8, p.467-477, World Scientific and Engineering Academy and Society, 2009.**Temur Jangveladze, Zurab Kiguradze**,*Finite Difference Scheme to a Nonlinear Integro-Differential Equation Associated with the Penetration of a Magnetic Field into a Substance*, FANDB'09: Proceedings of the 2nd WSEAS international conference on Finite differences, finite elements, finite volumes, boundary elements, p. 186–192, World Scientific and Engineering Academy and Society, 2009.**Maia Aptsiauri, Temur Jangveladze, Zurab Kiguradze**,*On Asymptotic Behavior of Solution of One Nonlinear One-Dimensional Integro-Differential Analogue of Maxwell’s System*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, V.23, p.5-10, Tbilisi University Press, 2009.**Temur Jangveladze, Zurab Kiguradze, Maia Nikolishvili**,*On Approximate Solution of One Nonlinear Two-Dimensional Diffusion System*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, V.23, p.42-45, Tbilisi University Press, 2009.**Temur Jangveladze, Zurab Kiguradze, Beny Neta**,*Large Time Behavior of Solutions and Finite Difference Scheme to a Nonlinear Integro-Differential Equation*, Computers & Mathematics with Applications, V.57, N5, p.799-811, Elsevier, 2009.**Temur Jangveladze, Zurab Kiguradze, Beny Neta**,*Finite Difference Approximation of a Nonlinear Integro-Differential System*, Applied Mathematics and Computation, V.215, N2, p.615-628, Elsevier, 2009.**Temur Jangveladze, Zurab Kiguradze, Beny Neta**,*Large Time Behavior of Solutions to a Nonlinear Integro-Differential System*, Journal of Mathematical Analysis and Applications, V.351, N1, p.382-391, Elsevier, 2009.**Temur Jangveladze, Giorgi Lobjanidze**,*On a Variational Statement of a Nonlocal Boundary Value Problem for a Fourth-Order Ordinary Differential Equation*, Differential Equations, V.45, N3, p.335-343, Springer, 2009.**Temur Jangveladze, Giorgi Lobjanidze**,*Variational Formulation of One Nonlocal Problem for Forth Order Ordinary Differential Equation*, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics, Vol. 22, 51-55, Tbilisi University Press, 2008.**Maia Aptsiauri, Temur Jangveladze, Zurab Kiguradze**,*On the Stabilization of Solution as $t\to\infty$ and Convergence of the Corresponding Finite Difference Scheme for One Nonlinear Integro-Differential Equation*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, V.22, p.15-19, Tbilisi University Press, 2008.**Temur Jangveladze, Zurab Kiguradze, Maia Nikolishvili**,*On Investigation and Numerical Solution of One Nonlinear Biological Model*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, V.22, p.46-50, Tbilisi University Press, 2008.**Temur Jangveladze, Zurab Kiguradze**,*Large Time Behavior of Solutions and Difference Schemes to Nonlinear Integro-Differential System Associated with the Penetration of a Magnetic Field into a Substance*, Applied Mathematics, Informatics, and Mechanics, V.13, N1, p.40-54, Tbilisi University Press, 2008.**Temur Jangveladze, Giorgi Lobjanidze**,*On Variational Formulation of Bitsadze-Samarskii Problem for Second Order Two-dimensional Elliptic Equation*, Applied Mathematics, Informatics, and Mechanics, V.13, N1, p.55-65, Tbilisi University Press, 2008.**Maia Aptsiauri, Temur Jangveladze, Zurab Kiguradze**,*Large Time Behavior of Solutions and Numerical Approximation of Nonlinear Integro-Differential Equation Associated with the Penetration of a Magnetic Field into a Substance*, Applied Mathematics, Informatics, and Mechanics, V.13, N 2, p.3-17, Tbilisi University Press, 2008.**Temur Jangveladze, Zurab Kiguradze**,*Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation*, Georgian Mathematical Journal, (the issue is dedicated to the memory of Prof. J.-L.Lions on the occasion of his 80th birthday anniversary), V.15, N3, p.531-539, De Gruyter, 2008.**Temur Jangveladze, Zurab Kiguradze**,*Asymptotic Behavior of the Solution to a Nonlinear Integro-Differential Diffusion Equation*, Differential Equations, V.44, N4, p.538-550., Springer, 2008.**Temur Jangveladze, Zurab Kiguradze**,*Large Time Asymptotics of Solutions to a Nonlinear Integro-Differential Equation*, Memoirs on Differential Equations and Mathematical Physics, V.42, p.35-48, Andrea Razmadze Mathematical Institute, 2007.**Temur Jangveladze, Zurab Kiguradze**,*On the Stabilization of Solutions of an Initial-boundary Value Problem for a Nonlinear Integro-differential Equation*, Differential Equations, V.43, N6, p.854-861, Springer, 2007.**Temur Jangveladze, Zurab Kiguradze, Giorgi Lobjanidze**,*On Variational Formulation and Decomposition Methods for Bitsadze-Samarskii Nonlocal Boundary Value Problem for Two-Dimensional Second Order Elliptic Equations*, Proceedings of I. Vekua Institute of Applied Mathematics, V.56-57, p.67-77, Tbilisi University Press, 2007.**Temur Jangveladze, Zurab Kiguradze**,*Asymptotics of a Solution of a Nonlinear System of Diffusion of a Magnetic Field into a Substance*, Siberian Mathematical Journal, V.47, N5, p.1058-1070, English translation: V.47, N5, p.867-878., Springer, 2006.**Temur Jangveladze, Zurab Kiguradze**,*On Nonlinear Integro-Differential Diffusion Equations Based on Maxwell’s System*, Proceedings of I. Vekua Institute of Applied Mathematics, V.56-57, p.56-66, Tbilisi University Press, 2006.**Maia Aptsiauri, Temur Jangveladze**,*The Asymptotic Behavior of Solutions and Finite Difference Scheme for One Nonlinear Integro-Differential Equation*, Bulletin of the Georgian National Academy of Sciences, V.174, N1, p.25-28, Georgian National Academy of Sciences, 2006.**Temur Jangveladze, Zurab Kiguradze**,*Domain Decomposition Method for Bitsadze-Samarskii Boundary Value Problem*, Trudy Tbiliss. Univ. Mat. Mekh. Astronom., V.354, N34-35, p.225-236, , 2005.**Temur Jangveladze**,*Investigation of the Asymptotic Behavior of Solution for One System of Nonlinear Integro-Differential Equations*, News Letters (Series A), Sukhumi Branch of I.Javakhishvili Tbilisi State University, V.3. p.25-28 (English summary), Tbilisi University Press, 2005.**Temur Jangveladze**,*On the Asymptotic Behaviour as $t\to\infty$ of Solutions of One Nonlinear Integro-Differential Parabolic Equation Arising in Penetration of a Magnetic Field into a Substance*, Rep. Enlarged Sess. Semin. I.Vekua Appl. Math., V.20, N1-3, p.8-11, Tbilisi University Press, 2005.**Temur Jangveladze, Zurab Kiguradze**,*Long Time Behavior of Solutions to Nonlinear Integro-Differential Equation*, Proceedings of I. Vekua Institute of Applied Mathematics, V.54-55, p.65-73, Tbilisi University Press, 2005.**Temur Jangveladze, Zurab Kiguradze**,*On One Nonlinear Integro-Differential Diffusion System*, Bulletin of the Georgian National Academy of Sciences, V.170, N1, p.42-45, Georgian National Academy of Sciences, 2004.**Temur Jangveladze**,*The Asymptotic Behavior as $t\to\infty$ of the Solution of One Nonlinear Integro-Differential Equation*, Bulletin of the Georgian National Academy of Sciences, V.170, N2, p.228-230, Georgian National Academy of Sciences, 2004.**Temur Jangveladze, Zurab Kiguradze**,*On One Nonlinear Integro-Differential Diffusion System*, Bulletin of the Georgian National Academy of Sciences, V.170, N1, p.42-45, Georgian National Academy of Sciences, 2004.**Temur Jangveladze, Zurab Kiguradze**,*Estimates of a Stabilization Rate as $t\to\infty$ of Solutions of a System of Nonlinear Integro-Differential Equations*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, V.18, N1-2, p.16-19, Tbilisi University Press, 2003.**Temur Jangveladze, Zurab Kiguradze**,*Estimates of a Stabilization Rate as $t\to\infty$ of Solutions of a Nonlinear Integro-Differential Diffusion System*, Applied Mathematics, Informatics, and Mechanics, V.8, N2, p.1-19, Tbilisi University Press, 2003.**Temur Jangveladze, Zurab Kiguradze**,*Estimates of a Stabilization Rate as $t\to\infty$ of Solutions of a Nonlinear Integro-Differential Equation*, Georgian Mathematical Journal, V.9, N1, p.57-70, De Gruyter, 2002.**Temur Jangveladze, Zurab Kiguradze**,*Domain Decomposition for Bitsadze-Samarskii Boundary Value Problem*, Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, V.16, N1-3, p.16-19, Tbilisi University Press, 2001.