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Degenerate Nonlinear Diffusion Equations

  • Book
  • © 2012

Overview

Authors:
  1. Angelo Favini

    1. Department of Mathematics, University of Bologna, Bologna, Italy

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    You can also search for this author in PubMed   Google Scholar

  2. Gabriela Marinoschi

    1. Inst. of Mathematical Statistics, and Applied Mathematics, Romanian Academy, Bucharest, Romania

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Existence for Parabolic–Elliptic Degenerate Diffusion Problems

    • Angelo Favini, Gabriela Marinoschi
    Pages 1-56

  3. Existence for Diffusion Degenerate Problems

    • Angelo Favini, Gabriela Marinoschi
    Pages 57-90

  4. Existence for Nonautonomous Parabolic–Elliptic Degenerate Diffusion Equations

    • Angelo Favini, Gabriela Marinoschi
    Pages 91-108

  5. Parameter Identification in a Parabolic–Elliptic Degenerate Problem

    • Angelo Favini, Gabriela Marinoschi
    Pages 109-133

  6. Back Matter

    Pages 135-143
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Bologna, Bologna, Italy

    Angelo Favini

  • Inst. of Mathematical Statistics, and Applied Mathematics, Romanian Academy, Bucharest, Romania

    Gabriela Marinoschi

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