Exponential Convergence to Time-Periodic Viscosity Solutions in Time-Periodic Hamilton-Jacobi Equations

Citation:

Kaizhi WANG.Exponential Convergence to Time-Periodic Viscosity Solutions in Time-Periodic Hamilton-Jacobi Equations[J].Chinese Annals of Mathematics B,2018,39(1):69~82
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Authors:

Kaizhi WANG;

Foundation:

This work was supported by the National Natural Science Foundation of China (No.11371167).
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

Classification:

35F25, 35B40, 37J99
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