Mathematical Problems in Linear Viscoelasticity

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.

Spis treści:
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.