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Multiscale Problems in Science and Technology

Challenges to Mathematical Analysis and Perspectives

  • Nenad Antonić
  • C. J. van Duijn
  • Willi Jäger
  • Andro Mikelić

Table of contents

  1. Front Matter
    Pages I-XII
  2. Björn Engquist, Olof Runborg
    Pages 129-150
  3. Thierry Clopeau, Jose Luis Ferrín, Andro Mikelic
    Pages 151-160
  4. Marina Kleptsyna, Andrey Piatnitski
    Pages 251-270
  5. Rainer Wehrse
    Pages 291-306
  6. Back Matter
    Pages 307-313

About these proceedings

Introduction

The International conference on Multiscale problems in science and technol­ ogy; Challenges to mathematical analysis and applications brought together mathematicians working on multiscale techniques (homogenisation, singular perturbation) and specialists from applied sciences who use these techniques. Our idea was that mathematicians could contribute to solving problems in the emerging applied disciplines usually overlooked by them and that specialists from applied sciences could pose new challenges for multiscale problems. Numerous problems in natural sciences contain multiple scales: flows in complex heterogeneous media, many particles systems, composite media, etc. Mathematically, we are led to study of singular homogenisation limits and the procedure is called upscaling or homogenisation. The processes to be up­ scaled are usually described by differential equations. For simple cases, when the differential equation is linear and the heterogeneities are periodic some progress has been made. However, most natural phenomena are described by nonlinear differential equations in a random nonhomogeneous medium and, despite an intensive development in recent years, there are many open problems. The objective of the conference was to bring together leading special­ ists from Europe and the United States and to discuss new challenges in this quickly developing field. Topics of the conference were Nonlinear Partial Differential Equations and Applied Analysis, with direct applications to the modeling in Material Sciences, Petroleum Engineering and Hydrodynamics.

Keywords

Analysis composite materials homogenisation layers mechanics modeling multiscale analysis oscillating solutions of PDEs

Editors and affiliations

  • Nenad Antonić
    • 1
  • C. J. van Duijn
    • 2
  • Willi Jäger
    • 3
  • Andro Mikelić
    • 4
  1. 1.Department of MathematicsUniversity of ZagrebZagrebCroatia
  2. 2.Dept. of Applied Analysis and Scientific ComputingCWI AmsterdamAmsterdamThe Netherlands
  3. 3.IWRUniversity of HeidelbergHeidelbergGermany
  4. 4.Analyse Numérique, Bât 101 U.F.R. MathématiquesUniversité Lyon 1Villeurbanne CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-56200-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43584-6
  • Online ISBN 978-3-642-56200-6
  • Buy this book on publisher's site
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