Electronic Journal of Qualitative Theory of Differential Equations (Jan 1999)
A memory type boundary stabilization of a mildly damped wave equation
Abstract
We consider the wave equation with a mild internal dissipation. It is proved that any small dissipation inside the domain is sufficient to uniformly stabilize the solution of this equation by means of a nonlinear feedback of memory type acting on a part of the boundary. This is established without any restriction on the space dimension and without geometrical conditions on the domain or its boundary.