HEAT STRUCTURE INTERACTION WITH VISCOELASTIC DAMPING: ANALYTICITY WITH SHARP ANALYTIC SECTOR, EXPONENTIAL DECAY, FRACTIONAL POWERS

摘要

We consider a heat structure interaction model where the structure is subject to viscoelastic (strong) damping. This is a preliminary step toward the study of a fluid structure interaction model where the heat equation is replaced by the linear version of the Navier Stokes equation as it arises in applications. We prove four main results: analyticity of the corresponding contraction semigroup (which cannot follow by perturbation); sharp location of the spectrum of its generator, which does not have compact resolvent, and has the point lambda = -1 in its continuous spectrum; exponential decay of the semigroup with sharp decay rate; finally, a characterization of the domains of fractional power related to the generator.