St. Petersburg Polytechnic University Journal: Physics and Mathematics Научно-технические ведомости СПбГПУ. Физико-математические науки 2304-9782, 2618-8686, 2405-7223 22 Matters of solvability and derivation of optimization systems in variational problems described by two-dimensional parabolic equations Вопросы разрешимости и получения оптимизационных систем в вариационных задачах, описываемых двумерными уравнениями параболического типа Pervadchuk Vladimir pervadchuk@mail.ru Shumkova Daria shumkova_darya@mail.ru Dektyarev Dmitry 10 09 2012 3 153 128 132

In this paper we obtain conditions for the solvability of the optimal control of two-dimensional nonlinear equation of parabolic type. In this case the function of optimal control is determined explicitly and depends on the solution of the resulting optimality system.

 optimal control partial differential equations system of optimality compromise control