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Nonlinear Diffusion Equations and Their Equilibrium States, 3

Proceedings from a Conference held August 20–29, 1989 in Gregynog, Wales

  • N. G. Lloyd
  • W. M. Ni
  • L. A. Peletier
  • J. Serrin

Table of contents

  1. Front Matter
    Pages i-x
  2. Sigurd B. Angenent
    Pages 21-38
  3. Michiel Bertsch, Roberta Dal Passo
    Pages 89-97
  4. Fabrice Bethuel, Jean-Michel Coron, Jean-Michel Ghidaglia, Alain Soyeur
    Pages 99-109
  5. J.R. Cannon, Paul Duchateau, Ken Steube
    Pages 153-169
  6. E. DiBenedetto, J. Manfredi, V. Vespri
    Pages 177-182
  7. Marek Fila, Josephus Hulshof, Pavol Quittner
    Pages 183-196
  8. D. Hilhorst, H. J. Hilhorst
    Pages 237-241
  9. S. Kamin, L. A. Peletier, J. L. Vazquez
    Pages 243-263
  10. Hans G. Kaper, Man Kam Kwong
    Pages 265-273
  11. Bernhard Kawohl
    Pages 275-286
  12. Tassilo Küpper, Charles A. Stuart
    Pages 287-297
  13. Howard A. Levine
    Pages 319-346
  14. John L. Lewis, Andrew Vogel
    Pages 347-374
  15. J. B. McLeod, C. A. Stuart, W. C. Troy
    Pages 391-405
  16. F. Merle, L. A. Peletier
    Pages 417-424
  17. Ana Rodríguez, Juan Luis Vázquez
    Pages 471-484
  18. Achilles Tertikas
    Pages 513-535
  19. Back Matter
    Pages 573-573

About this book

Introduction

Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math­ ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter­ est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = ~cp(U) + f(u). Here ~ denotes the n-dimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in space-time. FUn­ damental questions concern the existence, uniqueness and regularity of so­ lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up.

Keywords

Area Blowing up Finite behavior boundary element method design differential equation eXist equation interface interfaces partial differential equation similarity stability theorem

Editors and affiliations

  • N. G. Lloyd
    • 1
  • W. M. Ni
    • 2
  • L. A. Peletier
    • 3
  • J. Serrin
    • 2
  1. 1.Department of MathematicsUniversity College of WalesAberystwythUK
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  3. 3.Mathematical InstituteLeiden UniversityLeidenThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0393-3
  • Copyright Information Springer Science+Business Media New York 1992
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6741-6
  • Online ISBN 978-1-4612-0393-3
  • Buy this book on publisher's site
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