On the exponential stabilization of a thermo piezoelectric/piezomagnetic system

Abstract

This paper is motivated by a piezoelectric/piezomagnetic phenomenon in the presence of thermal effects. The evolution system we consider is linear and coupled between one hyperbolic , two elliptic and one parabolic equation. We show the equivalence between ``the exponential decay of the total energy of our system' and an ``observability inequality for an anisotropic elastic wave system' assuming that a geometric condition is satisfied. This geometric condition ensures that the elliptic operator associated with the mechanical part of our system has no eigenfunctions $ \Psi $ such that the divergence div (Λ $ \Psi $ ) = 0 in $\Omega$ where $ Λ $ denotes the thermal expansion tensor.