A characterization of the solutions of steady Hamilton-Jacobi equations

Gawtum Namah (1) , Mohammed Sbihi (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien

In this note, we propose to revisit the approximate stationary Hamilton-Jacobi equations and analyse the corresponding solutions following certain properties of the hamiltonian. This enables us to give a characterization of the zero set of the limiting solution. We also remark that the analysis can be applied for evolution equations with a time periodic source term.

Domaines: Equations aux dérivées partielles [math.AP]

Gawtum Namah, Mohammed Sbihi. A characterization of the solutions of steady Hamilton-Jacobi equations. 2010. ⟨hal-00495318⟩