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Birkhäuser

Nonlinear Diffusion Equations and Their Equilibrium States, 3

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

  • Conference proceedings
  • © 1992

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Editors:
  1. N. G. Lloyd

    1. Department of Mathematics, University College of Wales, Aberystwyth, UK

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  2. W. M. Ni

    1. School of Mathematics, University of Minnesota, Minneapolis, USA

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  3. L. A. Peletier

    1. Mathematical Institute, Leiden University, Leiden, The Netherlands

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  4. J. Serrin

    1. School of Mathematics, University of Minnesota, Minneapolis, USA

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 7)

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Table of contents (37 papers)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Blow Up in ℝn for a Parabolic Equation with a Damping Nonlinear Gradient Term

    • Liliane Alfonsi, Fred B. Weissler
    Pages 1-20

  3. Shrinking Doughnuts

    • Sigurd B. Angenent
    Pages 21-38

  4. Higher Approximations to Eigenvalues for a Nonlinear Elliptic Problem

    • F. V. Atkinson
    Pages 39-69

  5. Positive Solutions of Emden Equations in Cone-Like Domains

    • Catherine Bandle
    Pages 71-75

  6. Nonlinear Parabolic Equations Arising in Semiconductor and Viscous Droplets Models

    • Francisco Bernis
    Pages 77-88

  7. A Parabolic Equation with a Mean-Curvature Type Operator

    • Michiel Bertsch, Roberta Dal Passo
    Pages 89-97

  8. Heat Flows and Relaxed Energies for Harmonic Maps

    • Fabrice Bethuel, Jean-Michel Coron, Jean-Michel Ghidaglia, Alain Soyeur
    Pages 99-109

  9. Local Existence and Uniqueness of Positive Solutions of the Equation \(\Delta u + \left( {1 + \varepsilon \varphi \left( r \right)} \right){u^{\tfrac{{n + 2}}{{n - 2}}}} = 0\), in ℝn and a Related Equation

    • Gabrielle Bianchi, Henrik Egnell
    Pages 111-128

  10. Singularities of Solutions of a Class of Quasilinear Equations in Divergence Form

    • Marie-Françoise Bidaut-Veron
    Pages 129-144

  11. An Existence Result Via L s Regularity for Some Nonlinear Elliptic Equations

    • Lucio Boccardo, François Murat
    Pages 145-152

  12. Identifying a Time Dependent Unknown Coefficient in a Nonlinear Heat Equation

    • J.R. Cannon, Paul Duchateau, Ken Steube
    Pages 153-169

  13. On the Structure of Solutions for Some Semilinear Elliptic Equations

    • Kuo-Shung Cheng
    Pages 171-176

  14. A Note on Boundary Regularity for Certain Degenerate Parabolic Equations

    • E. DiBenedetto, J. Manfredi, V. Vespri
    Pages 177-182

  15. The Quenching Problem on the N-dimensional Ball

    • Marek Fila, Josephus Hulshof, Pavol Quittner
    Pages 183-196

  16. Global Solutions for a Class of Monge-Ampère Equations

    • Bruno Franchi
    Pages 197-214

  17. The Structure of Solutions near an Extinction Point in a Semilinear Heat Equation with Strong Absorption: A Formal Approach

    • V. A. Galaktionov, M. A. Herrero, J. J. L. Velázquez
    Pages 215-236

  18. On a conjecture by Hagan and Brenner

    • D. Hilhorst, H. J. Hilhorst
    Pages 237-241

  19. A Nonlinear Diffusion-Absorption Equation with Unbounded Initial Data

    • S. Kamin, L. A. Peletier, J. L. Vazquez
    Pages 243-263

  20. A Free Boundary Problem Arising in Plasma Physics

    • Hans G. Kaper, Man Kam Kwong
    Pages 265-273
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Keywords

About this book

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.

Reviews

"The book is worth reading for research workers in meteorology and geophysics, willing to deal with powerful tools of applied mathematics."
--MAP

Editors and Affiliations

  • Department of Mathematics, University College of Wales, Aberystwyth, UK

    N. G. Lloyd

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

    W. M. Ni, J. Serrin

  • Mathematical Institute, Leiden University, Leiden, The Netherlands

    L. A. Peletier

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