A renorming method for thermoelastic models

Abstract

We consider the coupled partial differential equations which arise in modeling linear thermoelastic structures. When this model is reformulated as an abstract Cauchy problem, it is known that the resulting solution semigroup is exponentially stable, and in certain cases it is analytic. In most cases, though, the infinitesimal generator of the semigroup does not satisfy a strict dissipative inequality. We construct a new norm, equivalent to the energy norm, for which a strict dissipative inequality is obtained. In the case of an analytic semigroup, the new norm allows the semigroup generator to become associated with a coercive esquilinear form.

Keywords:

• Thermoelasticity
• exponential stability
• analytic semigroup

AMS:

• 35B40
• 74F05
• 47D06