Stability of an abstract system of coupled hyperbolic and parabolic equations

Jianghao Hao, Zhuangyi Liu

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

In this paper, we provide a complete stability analysis for an abstract system of coupled hyperbolic and parabolic equations where A is a self-adjoint, positive definite operator on a Hilbert space H. For (α β) ∈ [0,1] × [0,1], the region of exponential stability had been identified in Ammar-Khodja et al. (ESAIM Control Optim Calc Var 4:577-593,1999). Our contribution is to show that the rest of the region can be classified as region of polynomial stability and region of instability. Moreover, we obtain the optimality of the order of polynomial stability.

Original languageEnglish (US)
Pages (from-to)1145-1159
Number of pages15
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume64
Issue number4
DOIs
StatePublished - Aug 1 2013

Keywords

  • Exponentialstability
  • Hyperbolic-parabolic equation
  • Polynomial stability
  • Semigroup

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