General decay of a Lord-Shulman thermoelastic system with nonlinear damping term

Abstract

In this article, we are interested in the study of a Lord-Shulman thermoelastic system with nonlinear damping term. We establish the well-posedness of the problem using the semigroup theory. By using the energy method and some properties of convex functions, we show that the dissipation given by this complementary control guarantees the general stability without imposing any restrictive growth assumption near the origin on the damping term. Furthermore, our result does not depend on any relationship between system parameters.