Variational Inequalities and Frictional Contact Problems

  • Anca┬áCapatina

Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 31)

Table of contents

  1. Front Matter
    Pages i-x
  2. Anca Capatina
    Pages 1-6
  3. Preliminaries

    1. Front Matter
      Pages 7-7
    2. Anca Capatina
      Pages 9-20
    3. Anca Capatina
      Pages 21-28
  4. Variational Inequalities

    1. Front Matter
      Pages 29-29
    2. Anca Capatina
      Pages 31-82
    3. Anca Capatina
      Pages 83-100
    4. Anca Capatina
      Pages 115-131
  5. Contact Problems with Friction in Elasticity

    1. Front Matter
      Pages 133-133
    2. Anca Capatina
      Pages 135-190
    3. Anca Capatina
      Pages 191-232
  6. Back Matter
    Pages 233-235

About this book

Introduction

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.

Keywords

Banach spaces Friction Functional analysis Hilbert spaces Optimal control Variational inequalities

Authors and affiliations

  • Anca┬áCapatina
    • 1
  1. 1.Institute of Mathematics "Simion Stoilow" of the Romanian AcademyBucharestRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-10163-7
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-10162-0
  • Online ISBN 978-3-319-10163-7
  • Series Print ISSN 1571-8689
  • Series Online ISSN 1876-9896
  • About this book
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