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A PDE approach to large-time asymptotics for boundary-value problems for nonconvex Hamilton-Jacobi equations. (English) Zbl 1243.35021
The authors study the large-time behavior of viscosity solutions of three types of initial-boundary value problems for Hamilton-Jacobi equations with non-convex Hamiltonians, specifically the Neumann/oblique derivative problem, the state constraint problem, and the Dirichlet problem. The approach relies on techniques specific to partial differential equations. A key tool is the asymptotically monotone property.

MSC:
35B40 Asymptotic behavior of solutions to PDEs
35F30 Boundary value problems for nonlinear first-order PDEs
35F21 Hamilton-Jacobi equations
35D40 Viscosity solutions to PDEs
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