Regularity Analysis For An Abstract System Of Coupled Hyperbolic And Parabolic Equations

Keywords

Analytic semigroup; Gevrey class semigroup; Hyperbolic-parabolic equations

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.

Publication Date

11-5-2015

Publication Title

Journal of Differential Equations

Volume

259

Issue

9

Number of Pages

4763-4798

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jde.2015.06.010

Socpus ID

84938214299 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84938214299

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