Materials with Memory: Initial-Boundary Value Problems for Constitutive Equations with Internal Variables

Hans-Dieter Alber (auth.)3540640665, 9783540640660

This book contributes to the mathematical theory of systems of differential equations consisting of the partial differential equations resulting from conservation of mass and momentum, and of constitutive equations with internal variables. The investigations are guided by the objective of proving existence and uniqueness, and are based on the idea of transforming the internal variables and the constitutive equations. A larger number of constitutive equations from the engineering sciences are presented. The book is therefore suitable not only for specialists, but also for mathematicians seeking for an introduction in the field, and for engineers with a sound mathematical background.

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Table of contents :
Introduction….Pages 1-5
Initial-boundary value problems for the inelastic behavior of metals….Pages 7-22
Constitutive equations of monotone type and generalized standard materials….Pages 23-44
Existence of solutions for constitutive equations of monotone type….Pages 45-56
Transformation of interior variables….Pages 57-73
Classification conditions….Pages 75-97
Transformation of rate independent constitutive equations….Pages 99-116
Application of the theory to engineering models….Pages 117-136
Open problems and related results….Pages 137-142