Applied Mathematics and Optimization, Vol.58, No.3, 393-410, 2008
Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints
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.