On a differential game in a system with distributed parameters

Abstract

We consider a game problem of approach for a system whose dynamics is described by a partial differential equation not of Kovalevskaya type, i.e., unsolved with respect to the time derivative. The equation with boundary conditions is written in a Hilbert function space in an abstract form as a differential operator equation. Using the method of resolving functionals, we obtain sufficient conditions for the approach of the system’s dynamical vector to a cylindrical terminal set. The results are exemplified by means of a model problem concerning a filtering process for a fluid in fractured porous rocks.