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Birkhäuser

Nonlinear Evolution Equations and Related Topics

Dedicated to Philippe Bénilan

  • Book
  • © 2004

Overview

Editors:
  1. Wolfgang Arendt

    1. Department of Applied Analysis, University of Ulm, Ulm, Germany

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  2. Haïm Brézis

    1. Analyse Numérique, Université Pierre et Marie Curie, B.C. 187, Paris Cedex 05, France
      Department of Mathematics Hill Center, Busch Campus, Rutgers University, Piscataway, USA

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  3. Michel Pierre

    1. Campus de Ker Lann, Antenne de Bretagne de l’ENS Cachan, Bruz, France

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  • Gives insight into new developments of nonlinear analysis by presenting a series of studies of recent mathematical models describing time evolution in physics, chemistry and other applications.
  • They are all related in some way to the mathematical work of the outstanding mathematician, Philippe Bénilan

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Table of contents (37 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Wolfgang Arendt, Haïm Brézis, Michel Pierre
    Pages 1-9

  3. Intrinsic metrics and Lipschitz functions

    • Francis Hirsch
    Pages 11-25

  4. Decay estimates for “anisotropic” viscous Hamilton-Jacobi equations in ℝN

    • Saïd Benachour, Philippe Laurençot
    Pages 27-37

  5. The Cauchy problem for linear growth functionals

    • F. Andreu, V. Caselles, J. M. Mazón
    Pages 39-65

  6. Asymptotic behaviour for the porous medium equation posed in the whole space

    • Juan Luis Vázquez
    Pages 67-118

  7. Dirichlet and Neumann boundary conditions: What is in between?

    • Wolfgang Arendt, Mahamadi Warma
    Pages 119-135

  8. The focusing problem for the Eikonal equation

    • S. B. Angenent, D. G. Aronson
    Pages 137-151

  9. Weak solutions and supersolutions in L 1 for reaction-diffusion systems

    • Michel Pierre
    Pages 153-168

  10. Global well-posedness and stability of a partial integro-differential equation with applications to viscoelasticity

    • S.-O. Londen, H. Petzeltová, J. Prüss
    Pages 169-201

  11. On some singular limits of homogeneous semigroups

    • P. Bénilan, L. C. Evans, R. F. Gariepy
    Pages 203-214

  12. Singular limit of changing sign solutions of the porous medium equation

    • Noureddine Igbida, Philippe Benilan
    Pages 215-224

  13. On the regularizing effect of strongly increasing lower order terms

    • Lucio Boccardo
    Pages 225-236

  14. Global smooth solutions for a quasilinear fractional evolution equation

    • Emilia Bazhlekova, Philippe Clément
    Pages 237-246

  15. On the uniqueness of solutions for nonlinear elliptic-parabolic equations

    • H. Gajewski, I. V. Skrypnik
    Pages 247-281

  16. Conservation laws with discontinuous flux functions and boundary condition

    • José Carrillo
    Pages 283-301

  17. Regularity of solutions of nonlinear Volterra equations

    • Volker G. Jakubowski, Petra Wittbold
    Pages 303-319

  18. Nonautonomous heat equations with generalized Wentzell boundary conditions

    • Jin Liang, Rainer Nagel, Ti-Jun Xiao
    Pages 321-331

  19. Maximal L p-regularity for elliptic operators with VMO-coefficients

    • Horst Heck, Matthias Hieber
    Pages 332-359

  20. Linearized stability for nonlinear evolution equations

    • Wolfgang M. Ruess
    Pages 361-373
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Keywords

About this book

Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of nonlinear evolution equations. The present volume is dedicated to him and contains research papers written by highly distinguished mathematicians. They are all related to Bénilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations. Special topics are Hamilton-Jacobi equations, the porous medium equation, reaction diffusion systems, integro-differential equations and visco-elasticity, maximal regularity for elliptic and parabolic equations, and the Ornstein-Uhlenbeck operator.

Also in this volume, the legendary work of Bénilan-Brézis on Thomas-Fermi theory is published for the first time.

 

Reviews

"The present volume is dedicated to the memory of Philippe Bénilan and contains about forty research articles which all previously appeared in the Journal of Evolution Equations. The topics covered are from Hamilton--Jacobi equations, the porous medium equation, reaction diffusion systems, integro-differential equations and viscoelasticity, maximal regularity for elliptic and parabolic equations, and the Ornstein--Uhlenbeck operator." (Monatshefle für Mathematik, G. Teschl, Wien)

Editors and Affiliations

  • Department of Applied Analysis, University of Ulm, Ulm, Germany

    Wolfgang Arendt

  • Analyse Numérique, Université Pierre et Marie Curie, B.C. 187, Paris Cedex 05, France

    Haïm Brézis

  • Department of Mathematics Hill Center, Busch Campus, Rutgers University, Piscataway, USA

    Haïm Brézis

  • Campus de Ker Lann, Antenne de Bretagne de l’ENS Cachan, Bruz, France

    Michel Pierre

Bibliographic Information

  • Book Title: Nonlinear Evolution Equations and Related Topics

  • Book Subtitle: Dedicated to Philippe Bénilan

  • Editors: Wolfgang Arendt, Haïm Brézis, Michel Pierre

  • DOI: https://doi.org/10.1007/978-3-0348-7924-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2004

  • Softcover ISBN: 978-3-7643-7107-4Published: 20 August 2004

  • eBook ISBN: 978-3-0348-7924-8Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XII, 807

  • Number of Illustrations: 5 b/w illustrations

  • Topics: Partial Differential Equations

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