Decay of the solution energy for a nonlinearly damped wave equation
| Author(s) : | Messaoudi SA, |
| Publisher : | KING FAHD UNIV PETROLEUM MINERALS |
| Publication Date : | 2001 |
| ISSN : | N/A |
| Abstract : | 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: 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 the energy of the solution decays exponentially if 2 less than or equal to m less than or equal to p., |