This book is motivated by stimulating problems in contact mechanics, emphasizing antiplane frictional contact with linearly elastic and viscoelastic materials. It focuses on the essentials with respect to the qualitative aspects of several classes of variational inequalities (VIs). Clearly presented, easy to follow, and well-referenced, this work treats almost entirely VIs of the second kind, with much of the material being state-of-the-art.
Applied mathematicians and advanced graduate students wishing to enter the field of VIs would benefit from this work as it sets out in detail basic features and results in the mathematical theory of contact mechanics. Researchers interested in applications of numerical analysis pertaining to VIs would also find the work useful. Assuming a reasonable knowledge of functional analysis, this volume is a must for graduate students, practitioners, and engineers engaged in contact mechanics.
Author(s): Andaluzia Matei, Mircea Sofonea (auth.)
Series: Advances in Mechanics and Mathematics 18
Edition: 1
Publisher: Springer-Verlag New York
Year: 2009
Language: English
Pages: 230
Tags: Partial Differential Equations; Operator Theory; Global Analysis and Analysis on Manifolds; Continuum Mechanics and Mechanics of Materials; Calculus of Variations and Optimal Control; Optimization
Front Matter....Pages 1-17
Front Matter....Pages 1-1
Preliminaries....Pages 1-17
Function Spaces....Pages 1-19
Front Matter....Pages 1-1
Elliptic Variational Inequalities....Pages 1-17
Evolutionary Variational Inequalities with Viscosity....Pages 1-14
Evolutionary Variational Inequalities....Pages 1-34
Volterra-type Variational Inequalities....Pages 1-17
Front Matter....Pages 1-1
Modeling of Contact Processes....Pages 1-18
Antiplane Shear....Pages 1-21
Front Matter....Pages 1-1
Elastic Problems....Pages 1-19
Viscoelastic Problems with Short Memory....Pages 1-11
Viscoelastic Problems with Long Memory....Pages 1-14
Back Matter....Pages 1-12
