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Nonlinear Diffusion Equations and Their Equilibrium States I

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

  • Conference proceedings
  • © 1988

Overview

Editors:
  1. W.-M. Ni

    1. School of Mathematics, University of Minnesota, Minneapolis, USA
      Mathematical Sciences Research Institute, Berkeley, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. L. A. Peletier

    1. Department of Mathematics and Computer Science, University of Leiden, The Netherlands

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    You can also search for this editor in PubMed   Google Scholar

  3. James Serrin

    1. School of Mathematics, University of Minnesota, Minneapolis, USA
      Mathematical Sciences Research Institute, Berkeley, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Mathematical Sciences Research Institute Publications (MSRI, volume 12)

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Table of contents (22 papers)

  1. Front Matter

    Pages iii-xiii
    Download chapter PDF

  2. On the Initial Growth of the Interfaces in Nonlinear Diffusion-Convection Processes

    • L. Alvarez, J. I. Diaz, R. Kersner
    Pages 1-20

  3. Large Time Asymptotics for the Porous Media Equation

    • Sigurd Angenent
    Pages 21-34

  4. Regularity of Flows in Porous Media: A Survey

    • D. G. Aronson
    Pages 35-49

  5. Ground States for the Prescribed Mean Curvature Equation: The Supercritical Case

    • F. V. Atkinson, L. A. Peletier, J. Serrin
    Pages 51-74

  6. Geometric concepts and methods in nonlinear elliptic Euler-Lagrange Equations

    • Ilya J. Bakelman
    Pages 75-107

  7. Nonlinear Parabolic Equations with Sinks and Sources

    • Catherine Bandle, Maria Assunta Pozio
    Pages 109-121

  8. Source-type Solutions of Fourth Order Degenerate Parabolic Equations

    • Francisco Bernis
    Pages 123-146

  9. Nonuniqueness and Irregularity Results for a Nonlinear Degenerate Parabolic Equation

    • M. Bertsch, R. Dal Passo, M. Ughi
    Pages 147-159

  10. Existence and Meyers estimates for solutions of a nonlinear parabolic variational inequality

    • Marco Biroli
    Pages 161-177

  11. Convergence to Traveling Waves for Systems of Kolmogorov-like Parabolic Equations

    • Maury Bramson
    Pages 179-190

  12. Symmetry Breaking in Semilinear Elliptic Equations with Critical Exponents

    • Chris Budd, John Norbury
    Pages 191-215

  13. Remarks on Saddle Points in the Calculus of Variations

    • Kung-Ching Chang
    Pages 217-235

  14. On the Elliptic Problem ∆u - |∇u|q + λu p = 0

    • M. Chipot, F. B. Weissler
    Pages 237-243

  15. Nonlinear elliptic boundary value problems: Lyusternik-Schnirelman theory, nodal properties and Morse index

    • Charles V. Coffman
    Pages 245-265

  16. Harnack-type Inequalities for some Degenerate Parabolic Equations

    • E. Di Benedetto
    Pages 267-271

  17. The Inverse Power Method for Semilinear Elliptic Equations

    • Alexander Eydeland, Joel Spruck
    Pages 273-286

  18. Radial Symmetry of the Ground States for a Class of Quasilinear Elliptic Equations

    • Bruno Franchi, Ermanno Lanconelli
    Pages 287-292

  19. Existence and Uniqueness of Ground State Solutions of Quasilinear Elliptic Equations

    • Bruno Franchi, Ermanno Lanconelli, James Serrin
    Pages 293-300

  20. Blow-up of solutions of nonlinear parabolic equations

    • Avner Friedman
    Pages 301-318
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Keywords

About this book

In recent years considerable interest has been focused on nonlinear diffu­ sion problems, the archetypical equation for these being Ut = D.u + f(u). Here D. 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 D.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.

Editors and Affiliations

  • School of Mathematics, University of Minnesota, Minneapolis, USA

    W.-M. Ni, James Serrin

  • Mathematical Sciences Research Institute, Berkeley, USA

    W.-M. Ni, James Serrin

  • Department of Mathematics and Computer Science, University of Leiden, The Netherlands

    L. A. Peletier

Bibliographic Information

  • Book Title: Nonlinear Diffusion Equations and Their Equilibrium States I

  • Book Subtitle: Proceedings of a Microprogram held August 25–September 12, 1986

  • Editors: W.-M. Ni, L. A. Peletier, James Serrin

  • Series Title: Mathematical Sciences Research Institute Publications

  • DOI: https://doi.org/10.1007/978-1-4613-9605-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1988

  • Hardcover ISBN: 978-0-387-96771-4Due: 24 June 1988

  • Softcover ISBN: 978-1-4613-9607-9Published: 30 December 2011

  • eBook ISBN: 978-1-4613-9605-5Published: 06 December 2012

  • Series ISSN: 0940-4740

  • Edition Number: 1

  • Number of Pages: XIII, 359

  • Topics: Analysis

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