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

Gawtum Namah; Mohammed Sbihi

doi:10.3934/dcdsb.2010.13.647

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2010, Volume 13, Issue 3: 647-664. Doi: 10.3934/dcdsb.2010.13.647

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

Gawtum Namah^1, and
Mohammed Sbihi^2,

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

Received: December 31, 2008

Revised: October 31, 2009

Published: September 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 35F25, 35B10; Secondary: 65M06.

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