# STABILIZATION OF WAVE EQUATION WITH NON-LINEAR DISSIPATIVE DAMPING ON THE BOUNDARY.

## Abstract

Let OMEGA be an open, bounded domain in R**m with a smooth boundary GAMMA equals GAMMA //0 mu GAMMA //1, where GAMMA //0 and GAMMA //1 are disjoint portions of the boundary. Let gamma (u) be a monotone increasing, possibly multivalued function defined on R**1. It is assumed that the graph of gamma (u) contains the origin, max vertical x vertical less than infinity and that gamma (u)u greater than 0 for u does not equal 0. A wave equation with nonlinear damping acting in the Neumann boundary conditions is considered. Some results are provided on asymptotic stability properties (when t yields infinity ) of the solutions to the equation.

## Publication Title

Proceedings of the IEEE Conference on Decision and Control

## Recommended Citation

Lasiecka, I.
(1987). STABILIZATION OF WAVE EQUATION WITH NON-LINEAR DISSIPATIVE DAMPING ON THE BOUNDARY..* Proceedings of the IEEE Conference on Decision and Control*, 2348-2349.
Retrieved from https://digitalcommons.memphis.edu/facpubs/5779