Mathematical Problems in Linear Viscoelasticity

Mauro Fabrizio, Angelo Morro9780898712667, 0898712661

Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.

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Table of contents :
Mathematical Problems in Linear Viscoelasticity……Page 2
SIAM Studies in Applied Mathematics……Page 3
ISBN 0-89871-266-1……Page 5
Contents……Page 6
Preface……Page 10
Introduction……Page 12
1 Preliminaries on Materials with Fading Memory……Page 16
2 Thermodynamics of Simple Materials……Page 29
3 Linear Viscoelasticity……Page 49
4 Existence, Uniqueness, and Stability……Page 79
5 Variational Formulations and Minimum Properties……Page 117
6 Wave Propagation……Page 155
7 Unbounded Relaxation Functions and Rayleigh Problem……Page 179
Appendix Precis of the Properties of the Relaxation Function……Page 193
References……Page 203
Index……Page 211