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.
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.