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Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

  • Book
  • © 2018

Overview

Authors:
  1. Messoud Efendiev

    1. Institute of Computational Biology, Helmholtz Center Munich, Neuherberg, Germany

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  • Contains new Liouville type results
  • Compares two different approaches
  • Characterizes asymptotics profile of solutions

Part of the book series: Fields Institute Monographs (FIM, volume 36)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Preliminaries

    • Messoud Efendiev
    Pages 1-70

  3. Trajectory Dynamical Systems and Their Attractors

    • Messoud Efendiev
    Pages 71-162

  4. Symmetry and Attractors: The Case N ≤ 3

    • Messoud Efendiev
    Pages 163-175

  5. Symmetry and Attractors: The Case N ≤ 4

    • Messoud Efendiev
    Pages 177-186

  6. Symmetry and Attractors

    • Messoud Efendiev
    Pages 187-198

  7. Symmetry and Attractors: Arbitrary Dimension

    • Messoud Efendiev
    Pages 199-224

  8. The Case of p-Laplacian Operator

    • Messoud Efendiev
    Pages 225-252

  9. Back Matter

    Pages 253-258
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Keywords

About this book

This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.

Reviews

“The author does a very good job with the difficult and somewhat unexpected task of pairing together elliptic PDE’s with dynamical systems methods specific to finite dimensions.” (Florin Catrina, zbMATH 1445.35005, 2020)

Authors and Affiliations

  • Institute of Computational Biology, Helmholtz Center Munich, Neuherberg, Germany

    Messoud Efendiev

Bibliographic Information

  • Book Title: Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

  • Authors: Messoud Efendiev

  • Series Title: Fields Institute Monographs

  • DOI: https://doi.org/10.1007/978-3-319-98407-0

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2018

  • Hardcover ISBN: 978-3-319-98406-3Published: 26 October 2018

  • Softcover ISBN: 978-3-030-07491-3Published: 26 January 2019

  • eBook ISBN: 978-3-319-98407-0Published: 17 October 2018

  • Series ISSN: 1069-5273

  • Series E-ISSN: 2194-3079

  • Edition Number: 1

  • Number of Pages: XVII, 258

  • Number of Illustrations: 3 b/w illustrations

  • Topics: Partial Differential Equations, Dynamical Systems and Ergodic Theory

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