Instability of coupled systems with delay

Abstract

We consider linear initial-boundary value problems that are a coupling like second-order thermoelasticity, or the thermoelastic plate equation or its generalization (the α-β-system introduced in [1, 26]). Now, there is a delay term given in part of the coupled system, and we demonstrate that the expected inherent damping will not prevent the system from not being stable; indeed, the systems will shown to be ill-posed: a sequence of bounded initial data may lead to exploding solutions (at any fixed time).