Exponential decay of solutions of a nonlinearly damped wave equation

Abstract.

The issue of stablity of solutions to nonlinear wave equations has been addressed by many authors. So many results concerning energy decay have been established. Here in this paper we consider the following nonlinearly damped wave equation $u_{{tt}} - \Delta u + a{\left( {1 + {\left| {u_{t} } \right|}^{{m - 2}} } \right)}u_{t} = bu|u|^{{p - 2}} ,$ a, b > 0, in a bounded domain and show that, for suitably chosen initial data, the energy of the solution decays exponentially even if m > 2.