General stabilization of a thermoelastic systems with a boundary control of a memory type

Abstract

"In this paper we consider an n-dimensional thermoelastic system, in a bounded domain, where the memory-type damping is acting on a part of the boundary and where the resolvent kernel k of ${-g^{\prime }(t)}/{g(0)} $ satisfies\linebreak $k^{\prime \prime }(t)\geq \gamma \left( t\right) (-k^{\prime }(t))^{p}$, $t\geq 0$, $1< p<\frac{3}{2} $. We establish a general decay result, from which the usual exponential and polynomial decay rates are only special cases. This work generalizes and improves earlier results in the literature."