American Institute of Mathematical Sciences

June  2007, 6(2): 389-410. doi: 10.3934/cpaa.2007.6.389

Time periodic viscosity solutions of Hamilton-Jacobi equations

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

Received  November 2005 Revised  September 2006 Published  March 2007

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.
Citation: Mihai Bostan, Gawtum Namah. Time periodic viscosity solutions of Hamilton-Jacobi equations. Communications on Pure & Applied Analysis, 2007, 6 (2) : 389-410. doi: 10.3934/cpaa.2007.6.389
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