Algorithm for numerical solution of the optimal control problem for the mathematical model of shallow water wave propagation

The article is devoted to the algorithm for numerical solution of the optimal control problem in a mathematical model of wave propagation in shallow water. The mathematical model is based on the IMBq equation (improved modified Boussinesq equation) and Dirichlet boundary conditions. The IMBq equation belongs to the semilinear Sobolev type equations of the second order. As it is known, the Cauchy problem for a Sobolev type equation is not solvable for arbitrary initial values. We consider a mathematical model with Showalter – Sidorov initial conditions that are more natural for it, making references to the Cauchy problem where necessary. The article also provides examples of computational experiments.