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Asymptotic solutions of Hamilton-Jacobi equations with state constraints. (English) Zbl 1178.35137
Summary: 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.

MSC:
35F25 Initial value problems for nonlinear first-order PDEs
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
35B40 Asymptotic behavior of solutions to PDEs
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