American Institute of Mathematical Sciences

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April  2000, 6(2): 361-380. doi: 10.3934/dcds.2000.6.361

Pursuit-evasion games with state constraints: dynamic programming and discrete-time approximations

Martino Bardi 1, , Shigeaki Koike 2, and  Pierpaolo Soravia 3,

1. 

Dipartimento di Matematica P. e A., Universita di Padova, via Belzoni 7, 35131 Padova
2. 

Department of Mathematics, Saitama University, 255 Shimo-Okubo, Urawa, Saitama 338-8570, Japan
3. 

Dipartimento di Matematica Pura e Applicata, Università di Padova, Belzoni 7, 1-35131, Padova, Italy

Received  December 1998 Revised  June 1999 Published  January 2000

In this paper we study the boundary value problem for the Hamilton-Jacobi-Isaacs equation of pursuit-evasion differential games with state constraints. We prove existence of a continuous viscosity solution and a comparison theorem that we apply to establish uniqueness of such a solution and its uniform approximation by solutions of discretized equations.
Keywords: comparison principle, state-constraint problem, Pursuit-evasion game, discrete-time approximation., viscosity solution.
Mathematics Subject Classification: 35F30, 49L20, 49L2.
Citation: Martino Bardi, Shigeaki Koike, Pierpaolo Soravia. Pursuit-evasion games with state constraints: dynamic programming and discrete-time approximations. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 361-380. doi: 10.3934/dcds.2000.6.361
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