Thermoelasticity with finite wave speeds
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書誌事項
Thermoelasticity with finite wave speeds
（Oxford mathematical monographs）
Oxford University Press, 2010
- : hbk
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注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
Generalized dynamic thermoelasticity is a vital area of research in continuum mechanics, free of the classical paradox of infinite propagation speeds of thermal signals in Fourier-type heat conduction. Besides that paradox, the classical dynamic thermoelasticity theory offers either unsatisfactory or poor descriptions of a solid's response at low temperatures or to a fast transient loading (say, due to short laser pulses). Several models have been developed and
intensively studied over the past four decades, yet this book, which aims to provide a point of reference in the field, is the first monograph on the subject since the 1970s.
Thermoelasticity with Finite Wave Speeds focuses on dynamic thermoelasticity governed by hyperbolic equations, and, in particular, on the two leading theories: that of Lord-Shulman (with one relaxation time), and that of Green-Lindsay (with two relaxation times). While the resulting field equations are linear partial differential ones, the complexity of the theories is due to the coupling of mechanical with thermal fields. The mathematical aspects of both theories - existence and
uniqueness theorems, domain of influence theorems, convolutional variational principles - as well as the methods for various initial/boundary value problems are explained and illustrated in detail and several applications of generalized thermoelasticity are reviewed.
目次
- Preface
- Introduction
- 1. Fundamentals of linear thermoelasticity with finite wave speeds
- 2. Formulations of initial-boundary value problems
- 3. Existence and uniqueness theorems
- 4. Domain of influence theorems
- 5. Convolutional variational principles
- 6. Central equation of thermoelasticity with finite wave speeds
- 7. Exact aperiodic-in-time solutions of Green-Lindsay theory
- 8. Kirchhoff type formulas and integral equations in Green- Lindsay theory
- 9. Thermoelastic polynomials
- 10. Moving discontinuity surfaces
- 11. Time-periodic solutions
- 12. Physical aspects and applications of hyperbolic thermoelasticity
- 13. Nonlinear hyperbolic rigid heat conductor of the Coleman type
- References
- Index
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