A notion of extremal solutions for time periodic Hamilton-Jacobi equations

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May 2010, 13(3): 647-664. doi: 10.3934/dcdsb.2010.13.647

A notion of extremal solutions for time periodic Hamilton-Jacobi equations

1.	Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France
2.	ENSMM, 26 chemin de l’Epitaphe, 25030 Besançon Cedex, France

Received January 2009 Revised November 2009 Published February 2010

Abstract
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This paper is concerned with time periodic solutions of Hamilton-Jacobi equations in which the hamiltonian is increasing wrt to the unknown variable. When the uniqueness of the periodic solution is not guaranteed, we define a notion of extremal solution and propose two different ways to attain it, together with the corresponding numerical simulations. In the course of the analysis, the ode case, where we show that things are rather explicit, is also visited.

Keywords: Hamilton-Jacobi equations, time periodic viscosity solutions, ode., asymptotic behaviour, approximation.

Mathematics Subject Classification: Primary: 35F25, 35B10; Secondary: 65M0.

Citation: Gawtum Namah, Mohammed Sbihi. A notion of extremal solutions for time periodic Hamilton-Jacobi equations. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 647-664. doi: 10.3934/dcdsb.2010.13.647

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