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Mathematical Sciences Research Institute Publications

Nonlinear Diffusion Equations and Their Equilibrium States I

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

Editors: Ni, W.-M., Peletier, L.A., Serrin, James (Eds.)

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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.

Table of contents (22 chapters)

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

    Alvarez, L. (et al.)

    Pages 1-20

  • Large Time Asymptotics for the Porous Media Equation

    Angenent, Sigurd

    Pages 21-34

  • Regularity of Flows in Porous Media: A Survey

    Aronson, D. G.

    Pages 35-49

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

    Atkinson, F. V. (et al.)

    Pages 51-74

  • Geometric concepts and methods in nonlinear elliptic Euler-Lagrange Equations

    Bakelman, Ilya J.

    Pages 75-107

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4613-9605-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-0-387-96771-4
  • Free shipping for individuals worldwide
  • This title is currently reprinting. You can pre-order your copy now.
Softcover $139.00
price for USA
  • ISBN 978-1-4613-9607-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

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
Series Volume
12
Copyright
1988
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4613-9605-5
DOI
10.1007/978-1-4613-9605-5
Hardcover ISBN
978-0-387-96771-4
Softcover ISBN
978-1-4613-9607-9
Series ISSN
0940-4740
Edition Number
1
Number of Pages
XIII, 359
Topics