Differential games in a Banach space on a fixed chain

Андрей Владимирович Чернов; Andrey Chernov

doi:10.17076/mgta_2020_3_22

Андрей Владимирович Чернов Нижегородский государственный университет им. Н.И. Лобачевского, Нижегородский государственный технический университет им. Р.Е. Алексеева
Andrey Chernov Nizhnii Novgorod State University, Nizhnii Novgorod State Technical University

DOI: https://doi.org/10.17076/mgta_2020_3_22

Keywords: differential game, nonlinear differential equation in a Banach space, Volterra set chain, piecewise program strategies, epsilon-equilibrium

Abstract

The paper is devoted to obtaining the sufficient conditions for existence of epsilon-equilibrium in the sense of piecewise program strategies in antagonistic games associated with nonlinear non-autonomous controlled differential equation in a Banach space and cost functional of a general enough form. The concept of piecewise program strategies in such a game is defined on the base of a concept of Volterra set chain for a right-hand operator of the corresponding integral equation controlled by the opponent players and according to a given partition of the time segment. As example we consider the game associated with a nonlinear pseudoparabolic partial differential equation governing the evolution of electric field in a semiconductor.