Exponential convergence to time-periodic viscosity solutions in time-periodic Hamilton-Jacobi equations

Abstract

Consider the Cauchy problem of a time-periodic Hamilton-Jacobi equation on a closed manifold, where the Hamiltonian satisfies the condition: The Aubry set of the corresponding Hamiltonian system consists of one hyperbolic 1-periodic orbit. It is proved that the unique viscosity solution of Cauchy problem converges exponentially fast to a 1-periodic viscosity solution of the Hamilton-Jacobi equation as the time tends to infinity.

Keywords

Hamilton-Jacobi equations / Viscosity solutions / Weak KAM theory

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