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| Exponential Convergence to Time-Periodic Viscosity Solutions in Time-Periodic Hamilton-Jacobi Equations |
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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 |
| Page view： 2118
Net amount： 1511 |
Authors： |
Kaizhi WANG; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11371167). |
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| 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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