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Initial data optimization problems for some classes of neutral functional differential equations: variation formulas, necessary optimality conditions, existence theorems (FR/89/5-107/12)


Funded by

SRNSFGShota Rustaveli National Science Foundation of Georgia

Start Date: 2013-04-15       End Date: 2015-04-15

For the quasi-linear neutral differential equations are proved: continuity of solution on the initial data and right-hand of equation; variation formulas of solution; necessary optimality conditions of the initial data and existence of an optimal initial data. For the linear neutral equation an algorithm finding of the initial data is constructed.

Project members:

Talks

  • Variation formulas of solution for differential equations taking into account delay function perturbation and initial data optimization problems, by Tamaz Tadumadze (Speaker), Nika Gorgodze at Second International Conference Mathematics in Armenia : Advances and Perspectives, 2013, Tsaghkadzor, Armenia.
  • Initial data optimization problems for one class of neutral functional differential equation with the continuous initial condition, by Tamaz Tadumadze (Speaker), Nika Gorgodze at International Workshop on the Qualitative Theory of Differential Equations "QUALITDE – 2013", 2013, Tbilisi, Georgia.
  • Sensitivity analysis of one class of controlled functional differential equation considering variable delay perturbation and the continuous initial condition, by Tamaz Tadumadze (Speaker) at International Workshop on the Qualitative Theory of Differential Equations, 2014, Tbilisi, Georgia.
  • Variation formulas of solution for a neutral functional- differential equation taking into account delay function perturbation and the discontinuous initial condition, by Tamaz Tadumadze (Speaker), Nika Gorgodze at Conference on Functional Differential Equations and Applications (FDEA 2014), 2014, Ariel, Israel.
  • Sensitivity analyses for some classes of controlled dynamical systems with time-delay, by Tamaz Tadumadze (Speaker) at Swedish-Georgian conference in analyses and dynamical system, 2015, Tbilisi, Georgia.

Publications

  • Tamaz Tadumadze, Nika Gorgodze, Variation formulas of a solution and initial data optimization problems for quasi-linear neutral functional differential equations with discontinuous initial condition, Mem.Differential Equations Math.Phys. 63, 1-77, Tbilisi University Press, 2014.
  • Tamaz Tadumadze, Nika Gorgodze, Variation formulas of solution for a class of controlled neutral functional- differential equations considering delay function perturbation and the continuous initial condition, Sem. I. Vekua Inst. Appl. Math., Rep. 40(2014), 45-49, Tbilisi University Press, 2014.
  • Tamaz Tadumadze, Abdeljalili Nachaoui, On the existence of an optimal element in quasi-linear neutral optimal problem, Sem. I. Vekua Inst. Appl. Math., Rep., 40, 50-67, Tbilisi University Press, 2014.
  • Tamaz Tadumadze, Conntinuous dependence of solutions of delay functional differential equations on the right-hand side and initial data considering delay perturbations, Georgin International Journal of Science and Technology, V. 6, No. 4 , 353-369, Nova Science Publishers, Inc., 2014.
  • Tamaz Tadumadze, Nika Gorgodze, Variation formulas of solution for a neutral functional-differential equation taking into account delay function perturbation and the discontinuous initial condition, Functional Differential Equations, V. 21, No. 3-4 , 147-154, Ariel University Center of Samaria, 2014.
  • Tamaz Tadumadze, Nika Gorgodze, Initial data optimization problem for the quasi-linear neutral functional differential equation with variable delays and the discontinuous initial condition, Proceedings of I. Vekua Institute of Applied Mathematics, 64 , 68-73, Tbilisi University Press, 2014.
  • Tamaz Tadumadze, Nika Gorgodze, Variation Formulas of Solution for a Functional Differential Equation with Delay Function Perturbation, Journal of Contemporary Mathematical Analysis , 49 (2), 53- 63, Springer, 2014.
  • Phridon Dvalishvili, Nika Gorgodze, Tamaz Tadumadze, Variation formulas of solution for neutral functional-differential equations with regard for the delay function perturbation and the continuous initial condition, Mem.Differential Equations Math.Phys. 64(2015), 163-168, Tbilisi University Press, 2015.
  • Tamaz Tadumadze, Inverse problem about transition in a fixed point for linear neutral neutral functional differential equations, Semin. I. Vekua Inst. Appl. Math., Rep., 41 , 59-62, Tbilisi University Press, 2015.
  • Nika Gorgodze, Tamaz Tadumadze, Ia Ramishvili, Continuous dependence of solution of a neutral functional differential equation on the right-hand side and initial data considering perturbations of variable delays, Georgian Math. J., 23 (4) , 519-535, De Gruyter, 2016.

Additional Information

In the framework of the project articles and abstracts are published in the scientific journals and in the proceedings of international conferences, including:
8.1. Gorgodze N. Well-possedness of the Cauchy problem for one class of neutral functional differential equation taking into account delay function perturbation. Sem. I. Vekua Inst. Appl. Math., Rep. , 39 (2013), 33-37.

8.2. Tadumadze T. , Gorgodze N., Variation Formulas of Solution for a Functional Differential Equation with Delay Function Perturbation. Journal of Contemporary Mathematical Analysis, 49 (2) (2014), 53-63.

8.3. Tadumadze T., Gorgodze N. Variation formulas of a solution and initial data optimization problems for quasi-linear neutral functional differential equations with discontinuous initial condition. Memoirs on Differential Equations and Mathematical Physics, 63(2014), 1-77.

8.4. Tadumadze T., Gorgodze N. Variation formulas of solution for a neutral functional-differential equation taking into account delay funtion perturbation and the discontinuous initial condition. Functionl Differential Equations, V. 21, No. 3-4 (2014), 147-154.

8.5. Tadumadze T. , Nachaoui A. On the existence of an optimal element in quasi-linear neutral optimal problem. Sem. I. Vekua Inst. Appl. Math., Rep, 40(2014), 50-67.

8.6. Tadumadze T., Gorgodze N. Initial data optimization problem for the quasi-linear neutral functional differential equation with variable delays and the discontinuous initial condition. Proceedings of I. Vekua Institute of Applied Mathematics, 64 (2014), 68-73.

8.7. Tadumadze T., Gorgodze N., Variation Formulas of Solution for Functional Differential Equations Taking Into Account Delay Function Perturbation and Initial Data Optimization Problems. Second International Conference “Mathematics in Armenia” Advances and Perspectives, 24-31 August 2013, Tsaghadzor, Armenia. 79-80.

8.8. Tadumadze T. On the well-possedness of the Cauchy problem for a functional differential equation taking into account variable delay perturbations. Proceedings of the International Conference Lie Groups, Differential Equations and Geometry, June, 10-22, 2013, Batumi, Georgia, v. 2, 132-136.

8.9. Tadumadze T., Gorgodze N. Initial data optimization problem for one class of neutral differential equation with the continuous initial condition. International Workshop on the Qualitative Theory of Differential Equations, December 20-22, 2013, Tbilisi, Georgia, Abstracts, 133-135.

8.10. Tadumadze T., Gorgodze N. Variation formulas of solution for a neutral functional- differential equation taking into account delay function perturbation and the discontinuous initial condition. Conference on Functional Differential Equations and Applications-FDEA 2014, Ariel, Israel, Abstracts, p. 45.
The scientific conference of the project was held within the framework of the 2nd International Tbilisi-Salerno Workshop on Modeling in Mathematics, March 16-18, 2015, TSU, Tbilisi. On the conference have been invited A. Nachaoui (University of Nantes, France), R. Cheruli, J. Felichi, A.R. Pharaioli (University of Salerno, Italy).
T. Tadumadze was on the scientific trip to Armenia, Italy and Israel.