Energy decay for the wave equation with a nonlinear weak dissipation

Abstract

We derive a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with a nonlinear dissipation $ \rho (u_{t}) $, where $ \rho (v) $ is a function like $ v/\sqrt{ 1+v^{2}}$. Since our dissipation is weak as $\vert u_{t}\vert $ tends to $ \infty $ we treat strong solutions rather than usual energy finite solutions.