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The Periodic Unfolding Method

Theory and Applications to Partial Differential Problems

  • Doina Cioranescu
  • Alain Damlamian
  • Georges Griso

Part of the Series in Contemporary Mathematics book series (SCMA, volume 3)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Unfolding in Fixed Domains

    1. Front Matter
      Pages 1-3
    2. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 5-59
    3. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 61-97
    4. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 99-149
  3. Unfolding in Perforated Domains

    1. Front Matter
      Pages 151-153
    2. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 155-198
    3. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 199-235
    4. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 237-253
  4. Partial Unfolding

    1. Front Matter
      Pages 255-257
    2. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 259-261
    3. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 263-279
  5. Unfolding for small obstacles and strange terms

    1. Front Matter
      Pages 281-283
    2. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 285-295
    3. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 297-353
  6. Linear Elasticity

    1. Front Matter
      Pages 355-357
    2. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 359-398
  7. An application: sharp error estimates

    1. Front Matter
      Pages 399-401
    2. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 403-419
    3. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 421-470
    4. Doina Cioranescu, Alain Damlamian, Georges Griso
      Pages 471-492
  8. Back Matter
    Pages 493-513

About this book

Introduction

This is the first book on the subject of the periodic unfolding method (originally called "éclatement périodique" in French), which was originally developed to clarify and simplify many questions arising in the homogenization of PDE's. It has since led to the solution of some open problems.

 Written by the three mathematicians who developed the method, the book presents both the theory as well as numerous examples of applications for partial differential problems with rapidly oscillating coefficients: in fixed domains (Part I), in periodically perforated domains (Part II), and in domains with small holes generating a strange term (Part IV).  The method applies to the case of multiple microscopic scales (with finitely many distinct scales) which is connected to partial unfolding (also useful for evolution problems). This is discussed in the framework of oscillating boundaries (Part III).  A detailed example of its application to linear elasticity is presented in the case of thin elastic plates (Part V).  Lastly, a complete determination of correctors for the model problem in Part I is obtained (Part VI).

This book can be used as a graduate textbook to introduce the theory of homogenization of partial differential problems, and is also a must for researchers interested in this field.

Keywords

Unfolding homogenization Linear Elasticity homogenization the periodic unfolding method. evolution problems oscillating boundaries linear elasticity

Authors and affiliations

  • Doina Cioranescu
    • 1
  • Alain Damlamian
    • 2
  • Georges Griso
    • 3
  1. 1.Laboratoire Jacques-Louis LIonsUniversity Pierre et Marie CurieParisFrance
  2. 2.Laboratoire d'Analyse et Mathématiques AppliquéesUniversité Paris-Est Créteil Val de MarneCreteil, CedexFrance
  3. 3.Laboratoire Jacques-Louis LIonsUniversity Pierre et Marie CurieParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-13-3032-2
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-13-3031-5
  • Online ISBN 978-981-13-3032-2
  • Series Print ISSN 2364-009X
  • Series Online ISSN 2364-0103
  • Buy this book on publisher's site