Pursuit Differential Game of Many Pursuers with Integral Constraints on Compact Convex Set

We study a pursuit differential game of many pursuers and one evader in the plane. We are given a compact convex subset of R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^2$$\end{document}, and the pursuers and evader move in this set. They cannot leave this set during the game. Control functions of players are subject to coordinate-wise integral constraints. If the state of a pursuer coincides with that of evader at some time, then we say that pursuit is completed. Pursuers try to complete the pursuit, and the aim of the evader is opposite. We obtain some conditions under which pursuit can be completed from any positions of the players in the given set. Moreover, we construct strategies for the pursuers. Also, we prove some properties of convex sets.