Degenerate Nonlinear Diffusion Equations

  • Angelo Favini
  • Gabriela Marinoschi

Part of the Lecture Notes in Mathematics book series (LNM, volume 2049)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Angelo Favini, Gabriela Marinoschi
    Pages 1-56
  3. Angelo Favini, Gabriela Marinoschi
    Pages 57-90
  4. Angelo Favini, Gabriela Marinoschi
    Pages 109-133
  5. Back Matter
    Pages 135-143

About this book

Introduction

The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain.
From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, coefficient identification, and to introduce relevant solving methods for each of them.

Keywords

35K35, 47Hxx, 35R35, 34C25, 49J20 degenerate nonlinear diffusion equations free boundary problems inverse problems parabolic boundary value problems

Authors and affiliations

  • Angelo Favini
    • 1
  • Gabriela Marinoschi
    • 2
  1. 1.Department of MathematicsUniversity of BolognaBolognaItaly
  2. 2.Inst. of Mathematical Statistics, and Applied MathematicsRomanian AcademyBucharestRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-28285-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-28284-3
  • Online ISBN 978-3-642-28285-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book