THERMOELASTICITY WITH ANTIDISSIPATION

We provide a complete stability analysis for the abstract differential system made by an antidamped wave-type equation, coupled with a dissipative heat-type equation{u(tt) + Au - gamma u(t) = pA(alpha)theta theta(t) + kappa A(beta)theta = -pA(alpha)u(t)where A is a strictly positive selfadjoint operator on a Hilbert space, gamma, kappa > 0, and both the parameters alpha and beta can vary between 0 and 1. The asymptotic properties of the associated solution semigroup are determined by the strength of the coupling, as well as the quantitative balance between the antidamping gamma and the damping kappa. Depending on the value of (alpha, beta) in the unit square, one of the following mutually disjoint situations can occur: either the related semigroup decays exponentially fast, or all the solutions vanish but not uniformly, or there exists a trajectory whose norm blows up exponentially fast as t -> infinity.