Analyticity of hybrid systems arising in visco and thermo elastic structures

Abstract

We consider two systems arising in a two-dimensional viscoelastic fluid-structure interaction, one of them coupled with a wave equation with interior damping of Kelvin–Voigt type. In the second model, the acoustic vibrations of the viscous fluid which fills the two-dimensional interior cavity are coupled with the mechanical vibrations of a one-dimensional thermoelastic beam. Therefore, the systems are related to the problem of the active control of noise in a cavity. Our main results are that the corresponding semigroups are analytic. In particular we show the exponential stability of the models.