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Multiscale Problems in Science and Technology

Challenges to Mathematical Analysis and Perspectives

  • Conference proceedings
  • © 2002

Overview

Editors:
  1. Nenad Antonić

    1. Department of Mathematics, University of Zagreb, Zagreb, Croatia

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  2. C. J. Duijn

    1. Dept. of Applied Analysis and Scientific Computing, CWI Amsterdam, Amsterdam, The Netherlands

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  3. Willi Jäger

    1. IWR, University of Heidelberg, Heidelberg, Germany

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  4. Andro Mikelić

    1. Analyse Numérique, Bât 101 U.F.R. Mathématiques, Université Lyon 1, Villeurbanne Cedex, France

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  • A group of top specialists presents results on multiscale
  • Includes supplementary material: sn.pub/extras

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Table of contents (14 papers)

  1. Front Matter

    Pages I-XII
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  2. Mathematical Tools for Studying Oscillations and Concentrations: from Young Measures to H-Measures and Their Variants

    • Luc Tartar
    Pages 1-84

  3. Statistical Mechanics of Violent Relaxation in Stellar Systems

    • Pierre-Henri Chavanis
    Pages 85-116

  4. On the Role of Interface Energies in the Description of Material Behavior

    • Gianpietro Del Piero
    Pages 117-128

  5. Projection Generated Homogenization

    • Björn Engquist, Olof Runborg
    Pages 129-150

  6. Derivation of the Diphasic Biot’s Law for an Elastic Solid Matrix Containing Isolated Fluid Drops

    • Thierry Clopeau, Jose Luis Ferrín, Andro Mikelic
    Pages 151-160

  7. Mesoscopic Models of Reaction-Diffusion Processes with Exclusion Mechanism

    • Flavius Guiaş
    Pages 161-173

  8. Two-Scale Models for Liquid-Solid Phase Transitions in Binary Material with Equiaxed Microstructure

    • Christof Eck, Peter Knabner
    Pages 175-187

  9. Asymptotic Behaviour of the Incompressible Newtonian Flow Through Thin Constricted Fracture

    • Olivier Gipouloux, Eduard Marušić-Paloka
    Pages 189-202

  10. Finite Dimensional Approximations for Elliptic Problems with Rapidly Oscillating Coefficients

    • Ana-Maria Matache, Christoph Schwab
    Pages 203-242

  11. The Failure of Uniform Exponential Decay for Boundary Layers

    • Maria Neuss-Radu
    Pages 243-250

  12. Homogenization of Random Nonstationary Convection-Diffusion Problem

    • Marina Kleptsyna, Andrey Piatnitski
    Pages 251-270

  13. Remarks on Γ-Convergence of Penalized Functionals of Ginzburg-Landau Type in One Dimension

    • Andrija Raguž
    Pages 271-282

  14. Homogenization of a Free Boundary Problem: The no-Slip Condition

    • Ben Schweizer
    Pages 283-290

  15. Radiative Transfer with Many Spectral Lines

    • Rainer Wehrse
    Pages 291-306

  16. Back Matter

    Pages 307-313
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, University of Zagreb, Zagreb, Croatia

    Nenad Antonić

  • Dept. of Applied Analysis and Scientific Computing, CWI Amsterdam, Amsterdam, The Netherlands

    C. J. Duijn

  • IWR, University of Heidelberg, Heidelberg, Germany

    Willi Jäger

  • Analyse Numérique, Bât 101 U.F.R. Mathématiques, Université Lyon 1, Villeurbanne Cedex, France

    Andro Mikelić

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