A reduction principle for coupled nonlinear parabolic-hyperbolic PDE
type: Item
instance of: scholarly article
title: A reduction principle for coupled nonlinear parabolic-hyperbolic PDE
zbMATH Open document ID: 1073.37088
author: I. D. Chueshov
published in: Journal of Evolution Equations
publication date: 2005-04-29T00:00:00Z
review text: This paper concerns coupled systems of abstract parabolic and hyperbolic equations of the type \[ \left. \begin{aligned} w_{tt}+\gamma w_t &+ Lw= F(w,w_t,u)\\ u_t+ \nu Au &= G(w,w_t,u)\end{aligned}\right\}\;w\in W,\;u\in U. \] Here, \(W\) and \(U\) are Hilbert spaces, \(L\) and \(A\) are linear positive selfadjoint operators on \(W\) and \(U\), respectively, and \(\gamma\geq 0\) and \(\nu> 0\) are parameters. Initial-boundary value problems for PDEs of thermoelasticity can be modeled in this way. Under appropriate continuity and growth conditions on the nonlinearities \(F\) and \(G\), it is proved that the parabolic equation can be excluded by means of an invariant exponentially attracting Lipschitz manifold.
reviewed by: Lutz Recke
Mathematics Subject Classification ID: 37L25
Mathematics Subject Classification ID: 37L15
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L90
Mathematics Subject Classification ID: 35K90
zbMATH DE Number: 2163365
zbMATH Keywords: abstract evolution system
zbMATH Keywords: invariant Lipschitz manifold
zbMATH Keywords: thermoelasticity
zbMATH Keywords: coupled systems
zbMATH Keywords: parabolic and hyperbolic equations
MaRDI profile type: Publication
full work available at URL: s00028-004-0175-6
OpenAlex ID: W2090300847
DOI: 10.1007/S00028-004-0175-6
description: scientific article; zbMATH DE number 2163365