Nonsmooth semipermeable Barriers, Isaacs' equation, and application to a differential game with one target and two players
type: Item
instance of: scholarly article
title: Nonsmooth semipermeable Barriers, Isaacs' equation, and application to a differential game with one target and two players
zbMATH Open document ID: 0907.90292
DOI: 10.1007/BF02683336
published in: Applied Mathematics and Optimization
publication date: 1999-03-02T00:00:00Z
review text: The author discusses barriers of a differential game. In this context, two players act on a dynamic system through two controls, the first trying to reach a target given in advance and the second trying to avoid this. Since the pioneering work of Isaacs it is well-known that if the boundary of the victory domain of one of the players is regular (a \(C^2\)-manifold for instance) this boundary has some semipermeability property and is the solution of some PDE. In this paper, a complete extension of this phenomenon to victory domains whose boundary are only the boundary of a closed set is presented. This approach allows to express the barriers as generalized solution of suitable PDE. This paper in some sense solves a problem unsolved since the beginning of the theory of differential games.
reviewed by: Marc Quincampoix
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 49J24
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 58C06
zbMATH DE Number: 1057312
zbMATH Keywords: barriers
zbMATH Keywords: differential game
zbMATH Keywords: target
zbMATH Keywords: semipermeability
author: Pierre Cardaliaguet
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1057312