Variational Inequalities with Applications: A Study of Antiplane Frictional Contact Problems: Advances in Mechanics and Mathematics, cartea 18

Background on Functional Analysis.- Preliminaries.- Function Spaces.- Variational Inequalities.- Elliptic Variational Inequalities.- Evolutionary Variational Inequalities with Viscosity.- Evolutionary Variational Inequalities.- Volterra-type Variational Inequalities.- Background on Contact Mechanics.- Modeling of Contact Processes.- Antiplane Shear.- Antiplane Frictional Contact Problems.- Elastic Problems.- Viscoelastic Problems with Short Memory.- Viscoelastic Problems with Long Memory.

From the reviews:
"The aim of the present outstanding book is to consider a wide set of problems arising in the mathematical modeling of mechanical systems under bilateral constraints. … This volume is primarily addressed to applied mathematicians working in the field of variational inequalities and their applications, especially those concerned with numerical aspects. … the book will also be useful for scientists from application areas, in particular, those from engineering and physics." (Ján Lovíšek, Mathematical Reviews, Issue 2009 j)

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.

Organization of the book into 4 parts makes it easy to concentrate on the topics Presentation is very clear, easy to follow, and well-referenced Presents the essentials of the theory of VIs and its applications to a class of interesting problems in contact mechanics Includes supplementary material: sn.pub/extras