On modified method of multistep coordinate descent for optimal control problem for semilinear Sobolev-type model

The paper describes a numerical method for solving the optimal control problem for a semilinear model of Sobolev-type. The method is based on both the modified projection Galerkin method and the method of multistep coordinate descent with memory. New numerical methods for solving nonlinear optimal control problems are need, because there exists a large number of applications and it is difficult to find their analytical solutions. We consider mathematical model of regulating potential distribution of speed of the filtered liquid free surface motion. In order to numerically investigate the mathematical model, we use the sufficient conditions for the existence of an optimal control by solutions of Showalter–Sidorov problem for semilinear Sobolev type equation with $s$-monotone and $p$-coercive operator. We present the results of computational experiment that demonstrate the work of the proposed numerical method.