Advances in Mechanics and Mathematics

Variational Inequalities and Frictional Contact Problems

Authors: Capatina, Anca

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  • Presents complex information in an accessible style
  • Supports assertions with specific proofs
  • Addresses abstract results on variational and quasi-variational inequalities
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  • ISBN 978-3-319-10163-7
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Hardcover $119.99
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  • ISBN 978-3-319-10162-0
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Softcover $109.99
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  • ISBN 978-3-319-35735-5
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About this book

Variational Inequalities and Frictional Contact Problems contains a carefully selected collection of results on elliptic and evolutionary quasi-variational inequalities including existence, uniqueness, regularity, dual formulations, numerical approximations and error estimates ones. By using a wide range of methods and arguments, the results are presented in a constructive way, with clarity and well justified proofs. This approach makes the subjects accessible to mathematicians and applied mathematicians. Moreover, this part of the book can be used as an excellent background for the investigation of more general classes of variational inequalities. The abstract variational inequalities considered in this book cover the variational formulations of many static and quasi-static contact problems. Based on these abstract results, in the last part of the book, certain static and quasi-static frictional contact problems in elasticity are studied in an almost exhaustive way. The readers will find a systematic and unified exposition on classical, variational and dual formulations, existence, uniqueness and regularity results, finite element approximations and related optimal control problems. This part of the book is an update of the Signorini problem with nonlocal Coulomb friction, a problem little studied and with few results in the literature. Also, in the quasi-static case, a control problem governed by a bilateral contact problem is studied. Despite the theoretical nature of the presented results, the book provides a background for the numerical analysis of contact problems.

The materials presented are accessible to both graduate/under graduate students and to researchers in applied mathematics, mechanics, and engineering. The obtained results have numerous applications in mechanics, engineering and geophysics. The book contains a good amount of original results which, in this unified form, cannot be found anywhere else.

Reviews

“This important book is unique in that it presents a profound mathematical analysis of general contact problems. … The monograph is written in an accessible and self-contained manner. It will be of interest to research mathematicians and science engineers working in solid and fluid mechanics and in optimization theory of partial differential equations. Moreover, it is suitable as a textbook for graduate courses in optimization of elliptic systems.” (Ján Lovíšek, Mathematical Reviews, April, 2015)


Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-319-10163-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-319-10162-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-3-319-35735-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Variational Inequalities and Frictional Contact Problems
Authors
Series Title
Advances in Mechanics and Mathematics
Series Volume
31
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-10163-7
DOI
10.1007/978-3-319-10163-7
Hardcover ISBN
978-3-319-10162-0
Softcover ISBN
978-3-319-35735-5
Series ISSN
1571-8689
Edition Number
1
Number of Pages
X, 235
Number of Illustrations
4 illustrations in colour
Topics