Analyticity of Thermo-Elastic Semigroups with Free Boundary Conditions

Abstract

We consider a thermo-elastic plate system where the elastic equation does not account for rotational forces. Of all canonical boundary conditions (B.C.), we focus on the most challenging case unsolved in the literature: that of free B.C., which are coupled. As in other simpler B.C.-cases, we show that the corresponding s.c. contraction semigroup (on a natural energy space) is analytic, and, hence, uniformly stable. The proof employs P.D.E. methods and estimates. Thus, this paper completes the authors' analysis [L-Tl], [L-T.2], spurred by the original important contribution [L-R.l], on analyticity of thermo-elastic semigroups with no rotational forces: under all canonical B.C., they are analytic, hence uniformly stable.

Publication Title

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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