LIST OF SELECTED PUBLICATIONS OF
GEORGE JAIANI
(Other transcriptions: Dzhaiani, Dzaiani)
On the
Deflections of Thin Wedge-shaped Shells, Bulletin of the Academy of Science of
the Georgian SSR, 65 (3), 543-546, 1972
(in Russian, Georgian and English summaries)
On One Problem of
an Elastic Wedge-shaped Body, Bulletin of the Academy of Science of the
Georgian SSR, 70 (3), 557-560, 1973
(in Russian, Georgian and English summaries)
On One Problem
for the Fourth Order Degenerate Equation, Bulletin of the Academy of Science of
the Georgian SSR, 75 (1), 17-20,
1974 (in Russian, Georgian and English summaries)
On a Wedge-shaped
Body Arbitrary Loaded Along the Cusped Edge, Bulletin of the Academy of Science
of the Georgian SSR, 75 (2), 309-312,
1974 (in Russian, Georgian and English summaries)
Arbitrary Loaded
Elastic Half-plane Whose Young's Modulus is Power Function of Depth, Materials
of the I All-union School in Theory and Numerical Methods in Shell and Plate
Theory, Tbilisi University Press, 351-361, 1975 (in Russian)
On a Wedge-shaped
Shell, Proceedings of X All-union Conference in Shell and Plate Theory,
Tbilisi: "Metsniereba", 94-101, 1975 (in Russian),
Riquier Problems
with Weight for a Fourth Order Degenerate Equation, Dokl., Akad. Nauk SSSR,
231 (6), 1285-1288, 1976 (in Russian),
Riquier Problems with Weight for a Certain Degenerate Equation of Fourth Order,
Soviet Math. Dokl., 17
(6), 1715- 1719, 1976
A Generalization
of the Poisson Formula in Case of a Half-plane for a Degenerate Equation of
Even Order, Dokl. Akad.Nauk SSSR, 235 (6),
1245-1248, 1977 (in Russian), A Generalization of the Half-plane Poisson
Formula for a Degenerate Equation of Even Order, Soviet Math.Dokl.18
(4), 1132-1135, 1977
Bending of a
Plate with Power Law Changing Stiffness, Annuaire Des Ecoles Superieures
Mechanique Technique, XII
(2), 15-19, 1977 (in Russian)
The Riquier Problem for a Degenerate Equation, Complex
Analysis and its Applications, Papers Dedicated to I.Vekua‘s 70-th Anniversary,
Moscow: Nauka Press, 209-216, 1978 (in Russian)
On Some Boundary Value Problems for Prismatic Cusped
Shells, in Theory of Shells, Koiter W.T. and Mikhailov G.K., Eds., North-Holland
Pub.Comp., 339-343, 1980
On a Physical Interpretation of Fichera's Function,
Acad.Naz.dei Lincei, Rend.della Sc.Fis.Mat.e Nat.,
S. VIII, Vol.LXVIII (fasc.5), 426-435, 1980
The Problem V for the Euler-Poisson-Darboux Equation,
Reports of Seminar of I.Vekua Institute of Applied Mathematics,
15, 77-83, 1981 (in Russian)
Boundary Value Problems of Mathematical Theory of
Prismatic Shells with Cusps, Proceedings of All-union Seminar in Theory and
Numerical Methods in Shell and Plate Theory, Tbilisi University Press, 126-142,
1984 (in Russian)
Problems with Discontinuous Boundary Conditions for
the Euler-Poisson-Darboux Equation, Reports of Seminar of I.Vekua Institute of
Applied Mathematics, 18, 74-77, 1984
(in Russian)
Approximate Solution of Boundary Value Problems in the
Case of the Euler-Poisson-Darboux Equation, Reports of Seminar of I.Vekua
Institute of Applied Mathematics, 18,
78-82, 1984 (in Russian)
On the Behaviour of a Solution of the Vekua Problem
for the Euler-Poisson-Darboux Equation in the Half-plane, Reports of Seminar of
I.Vekua Institute of Applied Mathematics, 19,
23-26, 1985 (in Russian)
Formulas of Schwarz Type for a Singular Differential
Equation, Bulletin of the Academy of Sciences of the Georgian SSR,
122 (3), 469-472, 1986 (in Russian,
Georgian and English summaries)
On the Influence of Coefficients of Junior Terms on
Posing of Boundary Value Problems for Elliptic Equations with Order
Degeneration, Reports of Enlarged Sessions of the Seminar of I.Vekua Institute
of Applied Mathematics, 2 (1), 31-34,
1986 (in Russian)
The Weighted Dirichlet Problem with Discontinuous
Boundary Data for the Euler-Poisson-Darboux Equation in a Half-Plane,
Proceedings of I.Vekua Institute of Applied Mathematics,
19, 38-59, 1987 (in Russian)
Weight Boundary Value Problems for a Linear Degenerate
Elliptic Equation of Second Order, Uspekhi Matematichskikh Nauk,
42, 4 (256), 174, 1987 (in Russian)
Bending of Prismatic Cusped Shell With Power Law
Changing Stiffness, Proceedings of the XIV All-union Conference in Shell and
Plate theory, Tbilisi University Press, 474-479, 1987 (in Russian)
Linear Elliptic Equations with Order Degeneration and
Prismatic Shells with Cusps, Proceedings of All-union Conference in Modern
Problems of Mathematical Physics, Tbilisi University Press,
1, 207-213, 1987 (in Russian)
The First Boundary Value Problem of Cusped Prismatic Shell
Theory in Zero Approximation of Vekua Theory, Proceedings of I.Vekua Institute
of Applied Mathematics, 29, 5-38,
1988 (in Russian, Georgian and English summaries)
On the Problem of Behaviour of Solutions of Boundary
Value Problems in the Neighbourhood of Discontinuity Points of Boundary Data,
Reports of Enlarged Sessions of the Seminar of I.Vekua Institute of Applied
Mathematics, 4 (1), 34-37, 1989
On a Way of Construction of Solutions of Boundary
Value Problems for Higher Order Equations, Rendiconti di Matematica, Serie VII,
10, 717-731, 1990
The Generalized Holmgren Problem for the Equation yDu+bu_{y}=0 in the Case of a Half-circle,
Reports of Enlarged Session of the Seminar of I.Vekua Institute of Applied
Mathematics of Tbilisi State University, 6
(1), 21-24, 1991
On Some Applications of Variational Methods in the
Theory of Bending of Prismatic Cusped Shells, Proceedings of I.Vekua Institute
of Applied Mathematics of Tbilisi State University,
47, 36-44, 1992
An Example of Non-unique Solvability of Fichera
Problem in the Classical Sense, Reports of Enlarged Session of the Seminar of
I.Vekua Institute of Applied Mathematics of Tbilisi State University,
8 (1), 31-34,1993
On a Way of Solution of BVPs for a Class of Third
Order Partial Differential Equations, Reports of Enlarged Session of the
Seminar of I.Vekua Institute of Applied Mathematics of Tbilisi State
University, 10 (1), 32-35, 1995
On a Generalization of the Keldysh Theorem, Georgian
Mathematical Journal, 2 (3), 291-297,
1995
Elastic Bodies with Non-smooth Boundaries – Cusped
Plates and Shells, Zeitschrift fuer Angewandte Mathematik und Mechanik,
76, Supplement 2, 117-120, 1996
The Main Boundary Value Problems of Bending of Cusped
Plate in Weighted Sobolev Spaces, Applied Mathematics and Informatics,
1 (1), 78-84, 1996
On a Modification of the Lax-Milgram Theorem, Reports
of Enlarged Session of the Seminar of I.Vekua Institute of Applied Mathematics
of Tbilisi State University , 12 (1),
5-8, 1997
On Boundary Value Problems for Conjugate Generalized
Harmonic Functions, Ricerche di Matematica,
47, fasc. 2, 231-256, 1998
On a Model of a Bar with Variable Thickness, BULLETIN
of TICMI, 2, 36-40, 1998 (for
electronic version see: http://www.viam.science.tsu.ge/others/ticmi)
On a Cylindrical Bending of a Prismatic Shell with Two
Cusped Edges Under Action of an Idial Fluid, BULLETIN of TICMI,
2, 30-34, 1998 (coauthor N.
Chinchaladze, for electronic version see:
http://www.viam.science.tsu.ge/others/ticmi)
Bending of an Orthotropic Cusped Plate, Appl. Math.
Inform., 4 (1), 29-65, 1999
Initial and Boundary Value Problems for Singular
Differential Equations and Applications to the Theory of Cusped Bars and
Plates, Complex methods for partial differential equations (ISAAC Serials, 6), Eds.: H. Begehr, O.
Celebi, W. Tutschke. Kluwer, Dordrecht, 113-149, 1999
Oscillation of an Orthotropic Cusped Plate, Reports of
Enlarged Session of the Seminar of I.Vekua Institute of Applied Mathematics of
Tbilisi State University, 14 (1), 24-31,
1999
On a Vibration of an Elastic Cusped Bar, BULLETIN of
TICMI, 4, 24-28, 2000 (coauthor S. Kharibegashvili,
for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)
The First Boundary Value Problem for the System of
Cusped Prismatic Shells in the First Approximation, Appl. Math. Inform.,
5 (2), 26-46, 2000 (with: G.
Devdariani, S. Kharibegashvili, D. Natroshvili)
On a Mathematical Model of Bars with Variable
Rectangular Cross-sections, ZAMM-Zeitschrift fuer Angewandte Mathematik und
Mechanik, 81 (3), 147-173, 2001
Application of Vekua's Dimension Reduction Method to
Cusped Plates and Bars, Bull. TICMI (Tbilisi International Centre of
Mathematics and Informatics), 5, 27-34,
2001 (for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)
Dynamical Problems in the (0,0) and (1,0)
Approximations of a Mathematical Model of Bars. In "Functional-Analytic
and complex Methods, Interactions, and Applications to PDEs". Proceedings
of the International Graz Workshop, Graz, Austria, 12-16 February 2001, World
Scientific, 188-248, 2001 (with S.S. Kharibegashvili)
On a Cusped Elastic Solid-Fluid Interaction Problem,
Appl. Math. Inform, 6 (2),
25-64, 2001 (Coauthor N. Chinchaladze)
Static and Dynamical Problems for a Cusped Beam,
Proceedings of I.Vekua Institute of Applied Mathematics of Tbilisi State
University, 52, 1-36, 2002
Relation of Hierarchical Models of Cusped Elastic
Plates and Beams to the Three-dimensional Models, Reports of the Seminar of
I.Vekua Institute of Applied Mathematics, 28,
31-39, 2002
Bending of a Cusped Plates on an Elastic Foundation,
Bulletin of TICMI, 8, 22-31, 2004
(for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)
Two-dimensional Hierarchical Models for Prismatic
Shells with Thickness Vanishing at the Boundary, Journal of Elasticity,
77 (2), 95-122, 2004 (with:
S. Kharibegashvili, D. Natroshvili, W.L. Wendland)
On Big Deflections of Cusped Plates, Bulletin of
TICMI, 9, 6-13, 2005 (with: N.
Chinchaladze)
Oscillation of Cusped Euler-Bernoulli Beams and
Kirchhoff-Love Plates, Hacettepe Journal of Mathematics and Statistics,
35 (1), 7-53, 2006 (with: A. Kufner)
A Cusped Prismatic Shell-like Body under the Action
of Concentrated Moments,
ZAMP-Zeitschrift fuer Angewandte Mathematik und Physik (DOI 10.1007/s
00033-006-6005-7, Online First, published online: 20 November, 2006, access: http://www.birkhauser.ch)
A
cusped Prismatic Shell-like Body with the Angular Projection under the Action
of a Concentrated Force, Rendiconti Academia Nazionale delle Scienze detta dei
XL, Memorie di Matematica e Applicazioni, 124^{ 0 }(2006),
XXX (facs. 1), 65-82
Some Degenerate Elliptic Systems and Applications to
Cusped Plates, Mathematische Nachrichten, 280
(4), 388-407, 2007 (with B.-Wolfgang Schulze)
On
Physical and Mathematical Moments and the Setting of Boundary Conditions for
Cusped Prismatic Shells and Beams, Proceedings of the IUTAM Symposium on Relation of Shell, plate, Beam, and 3D Models
Dedicated to Centenary of Ilia Vekua, 23-27 April, 2007, Tbilisi, Georgia.
IUTAM Bookseries, 9, 133-146, Editors G. Jaiani, P. Podio-Guidugli. Springer, 2008
On
a Nonlocal Boundary Value problem for a System of Singular Differential
Equations,
Applicable Analysis: An International Journal,
87 (1),
83 – 97, 2008; First published electronically on 19 December 2007, (DOI:
10.1080/00036810701729964, access:
http://www.tandf.co.uk/journals/titles/00036811.asp)
Existence
and Uniqueness Theorems for Cusped Prismatic Shells in the N-th Hierarchical
Model, Mathematical Methods in Applied Sciences,
31 (11), 1345-1367, 2008 (with N. Chinchaladze, R. Gilbert, G.
Jaiani, S. Kharibegashvili, D. Natroshvili, DOI 10.1002/mma.975,
access for electronic version:
http://www3.interscience.wiley.com/search/allsearch?mode=
viewselected&product=journal&ID=117905390& view_selected.x=111&view_selected.y=7,
Published Online: 4 Feb
2008)
Cylindrical
Bending of a Cusped Plate with Big Deflections, Journal of Mathematical
Sciences,
157 (1), 52-69, Springer, 2009, [Translated from Sovremennaya
Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications),
51, Differential Equations and Their
Applications, 2008] (with N. Chinchaladze) access:
http://www.springerlink.com/content/
bt22900q5v238682/?p=1af5abb4d88148f9b5c7775b1319afab&pi=2
Cusped
Elastic Beams under the Action of Stresses and Concentrated Forces. Applicable
Analysis, 89 (5), 757–774, 2010
(with Chinchaladze, N.;
Gilbert, R. P.;
Kharibegashvili, S.;
Natroshvili, D.), access:
http://www.tandf.co.uk/journals
Concentrated
contact interactions in cuspidate prismatic shell-like bodies,
Archive of Applied Mechanics, 81 (10),
1487-1505, 2011 (with Chinchaladze, N., Maistrenko, B., and Podio-Guidugli, P.)
Initial-boundary value problems for solid-fluid composite structures, Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 63 (4), 625-653, 2012 (with Chinchaladze, N.; Gilbert, R.; Kharibegashvili, S.; Natroshvili, D.)
Some Basic Boundary Value Problems of the Plane Thermoelasticity with Microtemperatures, Mathematical Methods in the Applied Sciences, Article first published online: 26 JUL 2012 (http://onlinelibrary.wiley.com/doi/10.1002/mma.2652 /abstract) DOI: 10.1002/mma.2652. 2012; 36 (8), 956–966, 2013 (with Bitsadze, L.)
Differential Hierarchical Models for Elastic Prismatic Shells with Microtemperatures. ZAMM - Z. Angew. Math. Mech., 95 (1), 77-90, 2015
Hierarchical Models for Prismatic Shells with Mixed Conditions on Face Surfaces. Bull. TICMI, 17 (2), 24-48, 2013 (for electronic version see: http://www.viam.science.tsu.ge/others/ticmi)
Differential Hierarchical Models for Elastic Prismatic Shells with Microtemperatures. ZAMM - Z. Angew. Math. Mech., 95 (1), 77-90, 2015
A Model of Layered Prismatic Shells. Continuum Mechanics and Thermodynamics, 28, 765-784, 2016 http://link.springer.com/article/10.1007%2Fs00161-015-0414-9
On basic problems for elastic prismatic shells with microtemperatures. ZAMM - Z. Angew. Math. Mech., 96 (9), 1082–1088, 2016 (with L. Bitsadze)
Vekua type hierarchical models for prismatic shells with mixed conditions on face surfaces. Composite Structures,152, 226-238, 2016
Antiplane strain (shear) of orthotropic non-homogeneous prismatic shell-like bodies. Archives of Mechanics, 69 (4-5), 1-12, 2017 (with N. Chinchaladze)
Basic problems of thermoelasticity with microtemperatures for the half-space. Journal of Thermal Stresses, DOI: 10.1080/01495739.2018.1464415, 2018 (with L. Bitsadze)
On micropolar elastic cusped prismatic shells. Transactions of A. Razmadze Mathematical Institute, 170, 376-384, 2016
Hierarchical models for viscoelastic Kelvin-Voigt prismatic shells with voids. Bulletin of TICMI, 21 (2), 33-44, 2017
Antiplane strain (shear) of orthotropic non-homogeneous prismatic shell-like bodies. Archives of Mechanics, 69 (4-5), 1-12, 2017 (with N. Chinchaladze)
Basic problems of thermoelasticity with microtemperatures for
the half-space. Journal of Thermal Stresses, 41 (9), 1101-1114, 2018 DOI: 10.1080/01495739.2018.1464415,
2018 (with L. Bitsadze)
On BVPs for piezoelectric transversely isotropic cusped bars.
Bulletin of TICMI, vol. 23, No. 1, 2019, pp. 35-66
Monographs
1. Solution of some Problems for a Degenerate Elliptic Equation of Higher Order and their Applications to Prismatic Shells, Tbilisi University Press, 1982, 178 p. (in Russian, Georgian and English summaries)
2. Euler-Poisson-Darboux Equation, Tbilisi University Press, 1984, 79 p. (in Russian, Georgian and English summaries)
3. Theory of Cusped Euler-Bernoulli Beams and Kirchoff-Love Plates, Lecture Notes of TICMI, 3, 2002, 132 p. (for electronic version see: http:// www.viam.science.tsu.ge/others/ticmi)
4. Hierarchical Models for Elastic Cusped Plates and Beams, Lecture Notes of TICMI, 4, 2003, 121 p. (with: S. Kharibegashvili, D. Natroshvili, W.L. Wendland, for electronic version see: http:// www.viam.science.tsu.ge /others/ticmi)
5. Cusped Shell-like Structures, SpringerBriefs in Applied Science and Technology, Springer-Heidelberg-Dordrecht-London-New York, 2011, 84 p.
6. Piezoelectric Viscoelastic Kelvin-Voigt Cusped Prismatic Shells, Lecture Notes of TICMI, 19, 2018, 83 p.
Textbooks
1.
Corso Introduttivo Alle Equazioni Integrali Singolari, Universita degli Studi
di Roma "La Sapienza", Dipartamento di Matematica-Istituto "G. Ca1stellnuovo",
1996, 97 p.
2. Mathematical Models of Mechanics of Continua, Tbilisi University Press, Tbilisi, 2004, 338 p. (in Georgian)
3. Advanced Mathematics, Part I: Calculus for Chemistry, Biology, and Life Sciences. Lecture Course, Tbilisi University Press, 2009, 111 p. (in Georgian)
4. Advanced Mathematics, Part II: Differential Models for Chemistry, Biology, and Life Sciences. Lecture Course, Tbilisi University Press, 2009, 127 p. (with N. Chinchaladze, in Georgian)
5. Mathematical Models of Mechanics of Continua (Second Edition), Tbilisi University Press, Tbilisi, 2018, 526 p. (in Georgian)
Edited Books
1. Mathematics, Informatics, and Their Applications in Natural Sciences and Engineering, Springer Proceedings in Mathematics & Statistics, vol. 276, Editors G. Jaiani, D. Natroshvili, Springer, 2019, 175 p.
2. Proceedings of the IUTAM Symposium on Relation of Shell, plate,
Beam, and 3D Models, Dedicated to Centenary of Ilia Vekua, 23-27 April, 2007, Tbilisi,
Georgia. IUTAM Bookseries,
Vol. 9, Editors G. Jaiani, P. Podio-Guidugli. Springer, 2008, 220p.
3. English-Georgian-Russian-German-French-Italian Glossary of Mathematical Terms, Edited by G.V. Jaiani (Compiler: J. Antidze, G. Datashvili, Ts. Gabiskiria, G. Jaiani), Lecture Notes of TICMI, Vol. 6, 2005, 227p.
4. Problems and Examples in Elementary Mathematics, Edited by G.V. Jaiani (Compiler: A. Ambroladze, G. Lobshanidze, N. Mchedlishvili, K. Shvania, T. Sasheniuk, K. Tsiskaridze, A. Kharazishvili, G. Jaiani, T. Jangveladze), Tbilisi, 1992, 270 p. (in Georgian)
5. Sovremennye problemy matematicheskoi fiziki. Tom I (Russian) [Current Problems in Mathematical Physics. Vol. I] Proceedings of All-Union Symposium held in Tbilisi, April 22-25, 1987. Edited by G.V. Jaiani and I.K. Kiguradze. Tbil. Gos. Univ., Tbilisi, 1987. 511 p.
6. Differential’nye uravneniya v chastnykh proizvodnykh I ikh prilozenia. (Russian) [Partial Differential Equations and Their Applications] Proceedings of All-Union Symposium held in Tbilisi, April 21-23, 1982. Edited by L.G. Magnaradze and G.V. Jaiani. Tbil. Gos. Univ., Tbilisi, 1986, 256 p.