HEAT-VISCOELASTIC PLATE INTERACTION: ANALYTICITY, SPECTRAL ANALYSIS, EXPONENTIAL DECAY

We consider a heat-plate interaction model where the 2-dimensional plate is subject to viscoelastic (strong) damping. Coupling occurs at the interface between the two media, where each components evolves. In this paper, we apply "low", physically hinged boundary interface conditions, which involve the bending moment operator for the plate. We prove three main results: analyticity of the corresponding contraction semigroup on the natural energy space; sharp location of the spectrum of its generator, which does not have compact resolvent, and has the point lambda = -1/rho in its continuous spectrum; exponential decay of the semigroup with sharp decay rate. Here analyticity cannot follow by perturbation.