Decay of the solution energy for a nonlinearly damped wave equation

Abstract EN

The issue of stablity of solutions to nonlinear wave equations has been addressed by many authors.

Thus, many results concerning energy decay have been established.

Here in this paper, we consider the following nonlinearly damped wave equation: utt- Am + a{ 1 +1 u, j m~2)ut+bu I u\p~2 = 0, a, b > 0, in a bounded domain, and show, for arbitrary initial data, that the energy of the solution decays exponentially if 2 < m < p.