Evolution Equations in Thermoelasticity: 1st Edition (Hardback) book cover

Evolution Equations in Thermoelasticity

1st Edition

By Reinhard Racke, Song Jiang

Chapman and Hall/CRC

318 pages

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Hardback: 9781584882152
pub: 2000-06-21
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Description

Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions. Through systematic work that began in the 80s, we now also understand the basic features of nonlinear systems. Yet some questions remain open, and the field has lacked a comprehensive survey that explores these past results and presents recent developments.

Evolution Equations in Thermoelasticity presents a modern treatment of initial value problems and of initial boundary value problems in both linear and nonlinear thermoelasticity, in one- and multi-dimensional spatial configurations. The authors provide the first self-contained presentation of the subject that offers both introductory parts accessible to graduate students and sophisticated sections valuable to experts.

Reviews

"Graduate students will appreciate that material previously published only in papers is collected in this book and experts will find some new results here."

-European Mathematical Society Newsletter, No. 40 (June 2001)

Table of Contents

DERIVATION OF THE EQUATIONS

WELL-POSEDNESS OF THE LINEARIZED SYSTEM AND GENERAL ASYMPTOTICS

Linear Well-Posedness

First Results on the Time-Asymptotic Behavior

ASYMPTOTIC BEHAVIOR FOR LINEARIZED ONE-DIMENSIONAL MODELS

Large Time Behavior

Bounded Domains

The Cauchy Problem

The Semi-Axis

Propagation of Singularities

ASYMPTOTIC BEHAVIOR FOR LINEARIZED MULTI-DIMENSIONAL MODELS

Large-Time Behavior

Bounded Domains

The Cauchy Problem

Isotropic Media

Cubic media

Propagation of singularities

LOCAL EXISTENCE

Initial Boundary Value Problems

The Cauchy Problem

NONLINEAR ONE-DIMENSIONAL THERMOELASTICITY

Bounded Domains

The Cauchy Problem

The Semi-Axis

Stationary Forces

Blow-up of Smooth Solutions for Large Data

Weak Solutions

NONLINEAR MULTI-DIMENSIONAL THERMOELASTICITY

Bounded Domains

The Cauchy Problem

Blow-Up

CONTACT PROBLEMS

Fully Dynamical Contact Problems

Quasi-Static Contact Problems

Linear Quasi-Static Problems

Quasi-Static Contact

Smoothing Property

RELATED RESULTS

Exponential Decay in the Case of Damping

Asymptotic Behavior of Solutions as ½x½®*

Numerical Analysis

APPENDIX

Existence Theory for Linear Equations

Existence for Linear Evolution Systems

Linear Hyperbolic Systems

Linear Parabolic Equations

Regularity for Linear Elliptic Systems and Inequalities

About the Series

Monographs and Surveys in Pure and Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
SCI040000
SCIENCE / Mathematical Physics