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Mathematical Problems in Linear Viscoelasticity

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By Mauro Fabrizio and Angelo Morro


1992 / ix + 203 pages / Hardcover / ISBN: 978-0-898712-66-7 / List Price $108.00 / SIAM Member Price $75.60 / Order Code AM12

Special Features
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.

This book is intended for graduate students and researchers in mathematics, physics, and engineering. It is appropriate for any course involving differential problems of mathematical physics along with general principles of continuum mechanics. The reader is required to have general familiarity with standard techniques of modern analysis and basic concepts in continuum thermodynamics.

Introduction; Part I: Preliminaries on Materials With Fading Memory; Part II: Thermodynamics of Simple Materials; Part III: Linear Viscoelasticity; Part IV: Existence, Uniqueness, and Stability; Part V: Variational Formulations and Minimum Properties; Part VI: Wave Propagation; Part VII: Unbounded Relaxation Functions and Rayleigh Problem; Appendix: Precis of the Properties of the Relaxation Function; References; Index.



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