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

We study the decay rate to 0, as t −→ +∞ of the solution of equation ψt −∆ψ + |ψ|p−1ψ = 0 with Neumann boundary conditions in a bounded smooth open connected domain of R where p > 1. We show that either ψ(t, ·) converges to 0 exponentially fast or ψ(t, ·) decreases like t 1 (p−1) .