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Sensitivity analysis of some classes neutral differential equations and optimal problems considering perturbations of delay parameters (YS-21-554)


Funded by

SRNSFGShota Rustaveli National Science Foundation of Georgia

Start Date: 2021-12-16       End Date: 2023-12-17

For the controlled quasi-linear neutral differential equations the continuity of solution with respect to initial data will be proved. The analytic relation between of solutions of the original and perturbed equations will be established. For the quasi-linear neutral optimal problem the existence of an optimal element will be proved. The dependence on perturbations of the existence of an optimal element and the continuity of a functional minimum will be investigated. For the neutral differential model of an economic growth and its corresponding optimal problem the sensitivity analysis will be carried out. Computer simulations of the test examples will be held.

Project members:

Talks

  • On the well-possedness of the Cauchy problem for the quasi-linear controlled neutral functional differential equation, by Tea Shavadze (Speaker) at International Conferenceon Mathematical Analysis and Applicationsin Science and Engineering ICMA2SC'22, ISEP Porto-Portugal, June 27 - 29,2022, 2022, Porto.
  • About Continuity of Solution on the Initial Data for a Neutral Differential Equation, by Tea Shavadze (Speaker) at Georgian Mathematical Union XII Annual International Conference, 2022, Batumi.
  • Delay Optimization Problem for One Class of Functional Differential Equation, by Tea Shavadze (Speaker) at Festival of Mathematics 2022, 2022, Ariel, Israel.
  • On the Representation Formula of Solution for a Class of Perturbed Controlled Neutral Functional-Differential Equation, by Tea Shavadze (Speaker), Tamaz Tadumadze at The Fourth International Conference „Modern Problems in Applied Mathematics“ (MPAM2023), 2023, Tbilisi, Georgia.
  • On the well-posedness of the Cauchy problem for one class of controlled neutral functional differential equation considering perturbation of the initial data, by Tea Shavadze (Speaker), Ia Ramishvili at XXXVII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, 2023, Tbilisi, Georgia.
  • On the Representation Formula of Solution for a Class of Perturbed Controlled Neutral Functional Differential equation, by Tea Shavadze (Speaker), Nika Gorgodze, Ia Ramishvili at The International Workshop on the Qualitative Theory of Differential Equations, 2023, Tbilisi, Georgia.
  • On the Representation of a Solution for the Perturbed Quasi- Linear Controlled Neutral Functional Differential Equation, by Tea Shavadze (Speaker), Tamaz Tadumadze at 17th Annual International Conference on Mathematics: Teaching, Theory & Applications, 2023, Athens, Greece.
  • Representation formulas of the First Variation of Solution for One Class of Neutral Functional-Differential Equation with the Continuous and Discontinuous Initial Conditions, by Tea Shavadze (Speaker), Tamaz Tadumadze at Global Conference on Education (GCEDU), 2023, Dubai, UAE.

Publications

  • Tea Shavadze, Tamaz Tadumadze, Abdeljalil Nachaoui, On the Coefficient of Sensitivity of a Controlled Differential Model of the Immune Response, Seminar of I. Vekua Institute of Applied Mathematics REPORTS, Tbilisi State University Press, 2022.
  • Tea Shavadze, Ia Ramishvili, On the Functional Integral Equation with the Two Types Controls, Reports of Qualitde-2022, Volume 1, 2022, Tbilisi State University Press, 2022.
  • Ia Ramishvili, Tea Shavadze, Tamaz Tadumadze, A Controlled Integral Equation and Properties of its Kernel, Bulletin of TICMI, 26(2), pp. 81–88, 2022, Tbilisi State University Press, 2022.
  • Medea Iordanishvili, Tea Shavadze, Tamaz Tadumadze, Necessary Optimality Conditions of Delay Parameters for the Nonlinear Optimization Problem with the Mixed Initial Condition., Commun. Optim. Theory 2023 (2023) 2, Mathematical Research Press, London, UK, 2023.
  • Tea Shavadze, Tamaz Tadumadze, On the Well-Possednis of the Cauchy Problem for a Neutral Controlled Functional Differential Equation, Functional Differential Equations, 29 (3- 4), 2023, Israel, Ariel University Press, 2023.
  • Nika Gorgodze, Ia Ramishvili, Tea Shavadze, On the Representation Formula of Solution for a Class of Perturbed Controlled Neutral Functional Differential equation, Reports of Qualitde-2023, Volume 2, 2023, Tbilisi State University Press, 2023.
  • Abdeljalil Nachaoui, Tea Shavadze, Tamaz Tadumadze, On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition, Georgian Math. J. 2024, De Gruyter , 2024.

Additional Information

The project plans to publish at least 2 articles in high ranking journals; Research trips abroad to international conferences and scientific research trips. It is also planned to participate in local international conferences.