Regularity analysis for an abstract system of coupled hyperbolic and parabolic equations

Jianghao Hao, Zhuangyi Liu, Jiongmin Yong

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

In this paper, we provide a complete regularity analysis for the following abstract system of coupled hyperbolic and parabolic equations. {utt=-Au+γAαw,wt=-γAαut-kAβw,u(0)=u0,ut(0)=v0,w(0)=w0, where A is a self-adjoint, positive definite operator on a complex Hilbert space H, and (α, β). ∈. [0, 1]. ×. [0, 1]. We are able to decompose the unit square of the parameter (α, β) into three parts where the semigroup associated with the system is analytic, of specific order Gevrey classes, and non-smoothing, respectively. Moreover, we will show that the orders of Gevrey class is sharp, under proper conditions.

Original languageEnglish (US)
Pages (from-to)4763-4798
Number of pages36
JournalJournal of Differential Equations
Volume259
Issue number9
DOIs
StatePublished - Nov 5 2015

Keywords

  • Analytic semigroup
  • Gevrey class semigroup
  • Hyperbolic-parabolic equations

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