Pursuit differential games of many players on surface of cylinder and cone - Karapanan, Piriatharisini (2022)
In this thesis, pursuit differential game problems taking place on the surface of cylinder and cone are studied. The mobility of the players are expressed by simple differential equations. In the first problem, we consider a pursuit differential game involving two pursuers and one evader on the surface of a cylinder. To solve this problem, we study an equivalent differential game of two groups of countably many pursuers and one group of countably many evaders in R2 for a fixed duration. We find an estimate for the value of the differential game on the cylinder. We construct strategies for pursuers that are admissible for which they guarantee the estimation for the value of the game. In a different approach, this differential game problem is solved in the half-space. Secondly, we consider a pursuit differential game of many pursuers and evaders on the surface of a cylinder. Similar to the first problem, we consider an equivalent differential game performed by many groups of countably many pursuers and many groups of countably many evaders in R2. For this problem, we find a sufficient condition that pursuit can be completed if the total resource of the pursuers remains greater than that of the evaders and construct admissible strategies for pursuers which satisfy the completion of pursuit. Furthermore, we investigate a pursuit differential game where many pursuers pursuing one evader on the surface of a cone. We study an equivalent differential game in a sector by unfolding the cone. We prove that pursuit can be completed by the pursuers for a finite time by obtaining a sufficient condition. Admissible pursuit strategies are constructed for the pursuers. One can say that, in brief, the three problems are approached by reducing the differential games in R3 to equivalent ones in R2.