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  • © 2004

Nonlinear Evolution Equations and Related Topics

Dedicated to Philippe Bénilan

Birkhäuser

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
    PDF

  2. Introduction

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

  3. Intrinsic metrics and Lipschitz functions

    • Francis Hirsch
    Pages 11-25

  5. The Cauchy problem for linear growth functionals

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

  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

  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

  14. Global smooth solutions for a quasilinear fractional evolution equation

    • Emilia Bazhlekova, Philippe Clément
    Pages 237-246

  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
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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.

 

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Keywords

  • Boundary value problem
  • Evolution equations
  • Partial differential equations
  • acoustic wave equation
  • hyperbolic equation
  • partial differential equation
  • wave equation
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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)
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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

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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: Differential Equations

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Access via your institution
eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-3-0348-7924-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 149.99
Price excludes VAT (USA)
Learn about institutional subscriptions