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.
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
Biography
Reinhard Racke, Song Jiang
"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)
