Rate of decay to 0 of the solutions to a nonlinear parabolic equation

Imen Ben Arbi (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We study the decay rate to 0, as t ->+\infty of the solution of equation \Phi_t - \Delta_\Phi + |\Phi|^(p-1)\Phi = 0 with Neumann boundary conditions in a bounded smooth open connected domain of R^n where p > 1. We show that either \Phi (t; .) converges to 0 exponentially fast or \Phi (t; .) decreases like t^(1/(p-1)).

Mots clés: Rate of decay; Parabolic equation

Domaines: Analyse numérique [cs.NA]

Imen Ben Arbi. Rate of decay to 0 of the solutions to a nonlinear parabolic equation. 2010. ⟨hal-00517387⟩