, Volume 58, Issue 3, pp 393-410
Date: 29 Mar 2008

Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints

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Abstract

We study Hamilton-Jacobi equations in a bounded domain with the state constraint boundary condition. We establish a general convergence result for viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations with the state constraint boundary condition to asymptotic solutions as time goes to infinity.