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We investigate the large-time behavior of three types of initial-boundaryvalue problems for Hamilton-Jacobi Equations with nonconvex Hamiltonians. Weconsider the Neumann or oblique boundary condition, the state constraintboundary condition and Dirichlet boundary condition. We establish generalconvergence results for viscosity solutions to asymptotic solutions as timegoes to infinity via an approach based on PDE techniques. These results areobtained not only under general conditions on the Hamiltonians but also underweak conditions on the domain and the oblique direction of reflection in theNeumann case.

A PDE approach to large-time asymptotics for boundary-value problems for nonconvex Hamilton-Jacobi Equations