Study of the objectives of boundary control and final observation for the mathematical model of non-linear filtration

The article is devoted to studying the problem of boundary control and final observation for a degenerate mathematical model of non-linear filtration, based on the Oskolkov equation, with the initial condition of Showalter-Sidorov. This model belongs to the class of semilinear models of the Sobolian type, in which the nonlinear operator is $p$-coercive and $s$-monotonic. The paper for the first time considers the problem of boundary control and final observation for the semilinear model of the Sobolian type and establishes the conditions of the existence of the control-state pair of the matter being studied.