Time periodic viscosity solutions of Hamilton-Jacobi equations

Mihai Bostan; Gawtum Namah

doi:10.3934/cpaa.2007.6.389

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2007, Volume 6, Issue 2: 389-410. Doi: 10.3934/cpaa.2007.6.389

This issue Previous Article Global existence and long-time behaviour for a singular integro-differential phase-field system Next Article Hardy type inequalities and Gaussian measure

Time periodic viscosity solutions of Hamilton-Jacobi equations

Mihai Bostan^1, and
Gawtum Namah^1,

1.
Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 route de Gray, Besançon, 25030 Cedex

Received: November 2005

Revised: September 2006

Published: June 2007

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Abstract

This paper discusses viscosity solutions of general Hamilton-Jacobi equations in the time periodic case. Existence results are presented under usual hypotheses. The main idea is to reduce the study of time periodic problems to the study of stationary problems obtained by averaging the source term over a period. These results hold also for almost-periodic viscosity solutions.

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Mathematics Subject Classification: Primary: 35F20; Secondary: 35B45.

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