Start Date: 2009-03-01 End Date: 2011-03-01
Existence theorems of the optimal initial data (initial moment, delay parameter, initial vector, initial function) are proved. Continuity of the minimum of functional is established with respect to perturbations of right-hand side of equation and integrand. Necessary conditions optimality of the initial data are proved. Constructed algorithm of the approximate solution of the linear inverse problem and its convergence is proved.
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. Tadumadze T., Arsenashvili A. Existence of optimal initial data and well-posedness with respect to functional for a class delay optimal problem. Simin. I. Vekua Inst. Appl. Math., Rep., 39, 2009, 71-73.
8.2. Tadumadze T. On the existence of an optimal element for a delay control problem. Nonlinear Analysis 73 (2010) 211-220.
8.3. Tadumadze T. Variation formulas of solution for nonlinear delay differential equations with taking into account perturbation of delay parameter and discontinuous initial condition. Georgian International Journal of Sciences and Technology, v. 3, no. 1 (2010), 53-71.
8.4. Tadumadze T., Nachaoui A. Variation formulas of solution for a controlled delay functional-differential equation considering delay perturbation. TWMS J. App. Eng. Math. V.1, N.1, 2011, 34-44.
8.5. Tadumadze T. Variation formulas of solution for a delay differential equation with taking into account delay perturbation and the continuous initial condition. Georgian Math. J. v.18 (2011), No. 2, 348-364.
8.6. Tadumadze T. Variation formulas for solution of delay differential equations with mixed initial condition and delay perturbation. Nonlinear Oscillations, V. 17, No. 4 (2014), 503-532.
8.7. T. Tadumadze T., Nachaoui A., Arsenashvili A. Existence of optimal initial data for a quasi-linear neutral differential equaion. Fifth Congress of Mathematicians of Georgia, Abstracts of Contributed Talks, Batumi / Kutaisi, October 9 – 12, 2009, 94 p.
8.8. Tadumadze T., Arsenashvili A. On the optimality of an initial data for delay differential equations. International Congress of Mathematicians, Abstracts of short Communications, Hyderabad, India , August 19-27, 2010, 586-587.
8.9. Tadumadze T. On the optimization of initial data for delay differential equations. The Third International Conference ,, Problems of Cybernetics and Informatics”, Volume III, September 6-8, 2010, Baku, Azerbaijan, 61-64.
In the framework of the project, scientific seminars was held three times, in the work of which participated: B. Mordukhovich (USA), L. Tepoyan (Armenia), A. Domoshnitsky (Israel), A. Nachaoui (France), A. Niftiev (Azerbaijan).
T. Tadumadze has been on scientific trips to India, USA and France.