Rate of decay to \(0\) of the solutions to a nonlinear parabolic equation (Q2428728)

Summary: We study the decay rate to 0 as \(t\rightarrow + \infty \) of the solution of the equation \( \psi_t-\Delta\psi + | \psi |^{p-1} \psi=0\) with Neumann boundary conditions in a bounded smooth open connected domain of \(\mathbb{R}^{n} \) where \(p>1\). We show that either \( \psi(t,\cdot)\) converges to 0 exponentially fast or \( \psi(t,\cdot)\) decreases like \(t^{-\frac{1}{(p-1)}}\).