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

Gawtum Namah (1) , Mohammed Sbihi (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

This paper is concerned with time periodic solutions of Hamilton J acobi 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.

Domaines: Equations aux dérivées partielles [math.AP]

Gawtum Namah, Mohammed Sbihi. A notion of extremal solutions for time periodic Hamilton-Jacobi equations. Discrete and Continuous Dynamical Systems - Series B, 2010, 13 (3), pp.647-664. ⟨10.3934/dcdsb.2010.13.647⟩. ⟨hal-00476304⟩