Decay of the solution energy for a nonlinearly damped wave equation

The issue of stablity of solutions to nonlinear wave equations has been add ressed by many authors. Thus, many results concerning energy decay have bee n established. Here in this paper, we consider the following nonlinearly da mped wave equation: u(tt) - Deltau + a(1 + \u(t)\ (m-2))u(t) + bu \u \ (p-2) = 0, a, b > 0, in a bounded domain, and show, for arbitrary initial data, that t he energy of the solution decays exponentially if 2 less than or equal to m less than or equal to p.