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Nonlinear Inclusions and Hemivariational Inequalities

Models and Analysis of Contact Problems

  • Stanisław Migórski
  • Anna Ochal
  • Mircea Sofonea

Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 26)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Background on Functional Analysis

    1. Front Matter
      Pages 1-1
    2. Stanisław Migórski, Anna Ochal, Mircea Sofonea
      Pages 3-22
    3. Stanisław Migórski, Anna Ochal, Mircea Sofonea
      Pages 23-49
    4. Stanisław Migórski, Anna Ochal, Mircea Sofonea
      Pages 51-91
  3. Nonlinear Inclusions and Hemivariational Inequalities

    1. Front Matter
      Pages 93-93
    2. Stanisław Migórski, Anna Ochal, Mircea Sofonea
      Pages 95-120
    3. Stanisław Migórski, Anna Ochal, Mircea Sofonea
      Pages 121-171
  4. Modeling and Analysis of Contact Problems

    1. Front Matter
      Pages 173-173
    2. Stanisław Migórski, Anna Ochal, Mircea Sofonea
      Pages 175-199
    3. Stanisław Migórski, Anna Ochal, Mircea Sofonea
      Pages 201-240
    4. Stanisław Migórski, Anna Ochal, Mircea Sofonea
      Pages 241-265
  5. Back Matter
    Pages 267-285

About this book

Introduction

Nonlinear Inclusions and Hemivariational Inequalities presents a broad insight into the theory of inclusions, hemivariational inequalities, and their applications to Contact Mechanics. The content of this volume gathers recent results which are published here for the first time and gives a largely self-contained and rigorous introduction to mathematical analysis of contact problems. The book will be of particular interest to students and young researchers in applied and pure mathematics, civil, aeronautical and mechanical engineering, and may also prove suitable as a supplementary text for an advanced one or two semester specialized course in mathematical modeling.

 

This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of Contact Mechanics. It covers both abstract existence and uniqueness results as well as the study of specific contact problems, including their modeling and variational analysis. New mathematical methods are introduced and applied in the study of nonlinear problems, which describe the contact between a deformable body and a foundation.

 

The text is divided into three parts. Part I, entitled Background of Functional Analysis, gives an overview of nonlinear and functional analysis, function spaces, and calculus of nonsmooth operators. The material presented may be useful to students and researchers from a broad range of mathematics and mathematical disciplines. Part II concerns Nonlinear Inclusions and Hemivariational Inequalities and is the core of the text in terms of theory. Part III, entitled Modeling and Analysis of Contact Problems shows applications of theory in static and dynamic contact problems with deformable bodies, where the material behavior is modeled with both elastic and viscoelastic constitutive laws. Particular attention is paid to the study of contact problems with piezoelectric materials. Bibliographical notes presented at the end of each part are valuable for further study.

Keywords

Clarke subdifferential hemivariational inequality piezoelectricity static and dynamic contact problem stationary and evolutionary inclusions

Authors and affiliations

  • Stanisław Migórski
    • 1
  • Anna Ochal
    • 2
  • Mircea Sofonea
    • 3
  1. 1., Faculty of Mathematics and Computer ScieJagiellonian UniversityKrakówPoland
  2. 2., Faculty of Mathematics and Computer ScieJagiellonian UniversityKrakówPoland
  3. 3., Laboratoire de Mathématiques, Physique eUniversité de PerpignanPerpignanFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-4232-5
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-4231-8
  • Online ISBN 978-1-4614-4232-5
  • Series Print ISSN 1571-8689
  • Series Online ISSN 1876-9896
  • Buy this book on publisher's site