Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors

by Yuming Qin

Overview

This book presents recent results concerning the global existence in time, the large-time behaviour, decays of solutions and the existence of global attractors for some nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations arising from physics, mechanics and material science, such as the compressible Navier-Stokes equations, thermo(visco)elastic systems and elastic systems. To keep the book as self-contained as possible, the first chapter introduces to the needed results and tools from functional analysis, Sobolev spaces, differential and integral inequalities in analysis, and the theory of semigroups of linear operators and of global attractors.

Product Details

ISBN-13:	9783764388133
Publisher:	Birkhäuser Basel
Publication date:	09/25/2008
Series:	Operator Theory: Advances and Applications , #184
Edition description:	2008
Pages:	468
Product dimensions:	6.70(w) x 9.30(h) x 1.20(d)

Table of Contents

Preliminary.- A One-dimensional Nonlinear Viscous and Heat-conductive Real Gas.- A One-dimensional Polytropic Viscous and Heat-conductive Gas.- A Polytropic Ideal Gas in Bounded Annular Domains in .- A Polytropic Viscous Gas with Cylinder Symmetry in .- One-dimensional Nonlinear Thermoviscoelasticity.- A Nonlinear One-dimensional Thermoelastic System with a Thermal Memory.- One-dimensional Thermoelastic Equations of Hyperbolic Type.- Blow-up for the Cauchy Problem in Nonlinear One-dimensional Thermoelasticity.- Large-Time Behavior of Energy in Multi-Dimensional Elasticity.

Editorial Reviews

From the reviews:

“The monograph is focused on presentation of recent results on some nonlinear parabolic-hyperbolic systems of partial differential equations arising from physics, mechanics and material science. Most of the results presented in this book are based on the original research of the author starting in 1997. … The book is self-contained and the material is well organized for reading. It contains all necessary tools and background results enabling the reader to grasp the technical points easily.” (Daniel Sevcovic, Zentralblatt MATH, Vol. 1173, 2009)

From the Publisher