Investigation of various types of control problems for one nonlinear model of filtration

A wide class of mathematical physics problems can be considered within the framework of semi-linear Sobolev type equations, which describe various processes (for example deformation processes, processes occurring in semiconductors, processes of oscillatory motion propagation in various media, and so on). The article is devoted to the study of control problems (optimal, start and rigid) of one mathematical model of Sobolev type, which is based on the equation describing the process of changing the concentration potential of a viscoelastic fluid filtered in a porous medium (the process of nonlinear diffusion of matter). We find the sufficient conditions under which there exists a solution to the control problem of the model under study. An algorithm for the numerical solution method is constructed and a computational experiment is presented.