Heat-structure interaction with viscoelastic damping: Analyticity with sharp analytic sector, exponential decay, fractional powers
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 λ = -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.
Communications on Pure and Applied Analysis
Lasiecka, I., & Triggiani, R. (2016). Heat-structure interaction with viscoelastic damping: Analyticity with sharp analytic sector, exponential decay, fractional powers. Communications on Pure and Applied Analysis, 15 (5), 1515-1543. https://doi.org/10.3934/cpaa.2016001