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Nonlinear Diffusion Equations and Their Equilibrium States II

Proceedings of a Microprogram held August 25–September 12, 1986

  • W.-M. Ni
  • L. A. Peletier
  • James Serrin

Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 13)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Chunqing Lu, William C. Troy
    Pages 123-137
  3. Paul H. Rabinowitz
    Pages 217-233
  4. Victor L. Shapiro
    Pages 255-272
  5. J. Smoller, A. G. Wasserman
    Pages 273-287
  6. A. M. Stuart
    Pages 295-313
  7. Laurent Véron
    Pages 333-365

About these proceedings

Introduction

In recent years considerable interest has been focused on nonlinear diffu­ sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu­ clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com­ bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome­ ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc­ ture of the nonlinear function f(u) influences the behavior of the solution.

Keywords

Fusion Mathematica Scala behavior curvature differential equation equation form function genetics metrics online partial differential equation stability

Editors and affiliations

  • W.-M. Ni
    • 1
    • 2
  • L. A. Peletier
    • 3
  • James Serrin
    • 1
    • 2
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Mathematical Sciences Research InstituteBerkeleyUSA
  3. 3.Department of Mathematics and Computer ScienceUniversity of LeidenThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-9608-6
  • Copyright Information Springer-Verlag New York 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9610-9
  • Online ISBN 978-1-4613-9608-6
  • Series Print ISSN 0940-4740
  • Buy this book on publisher's site