Evolution Equations in Thermoelasticity

Evolution Equations in Thermoelasticity

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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.show more

Product details

  • Hardback | 320 pages
  • 162.1 x 242.3 x 22.1mm | 632.01g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 1584882158
  • 9781584882152

Review quote

"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)show more

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 1/2x1/2(R)* 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 Inequalitiesshow more