Exponential stability of a nondissipative, compressible flow-structure PDE model


Avalos G., Geredeli P. G.

JOURNAL OF EVOLUTION EQUATIONS, vol.20, no.1, pp.1-38, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1007/s00028-019-00513-9
  • Title of Journal : JOURNAL OF EVOLUTION EQUATIONS
  • Page Numbers: pp.1-38

Abstract

In this work, a result of exponential stability is obtained for solutions of a compressible flow-structure partial differential equation (PDE) model which has recently appeared in the literature. In particular, a compressible flow PDE and the associated state equation for the pressure variable, each evolving within a three-dimensional domain O, are coupled to a fourth-order plate equation which holds on a flat portion omega of the boundary partial differential O. Moreover, since this coupled PDE model is the result of a linearization of the compressible Navier-Stokes equations about an arbitrary state, the flow PDE component contains a nonzero ambient flow profile U and will generally be nondissipative. By way of obtaining the aforesaid exponential stability, a "frequency domain" approach is adopted here, an approach which is predicated on obtaining a uniform estimate on the resolvent of the associated flow-structure semigroup generator.