Variational Inequalities with Applications

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.

• antiplane shear
• contact mechanics
• elastic problems
• function spaces
• mechanics
• modeling
• visoelastic problems
• partial differential equations

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)

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