Abstract Parabolic Evolution Equations and their Applications

  • Atsushi Yagi

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Atsushi Yagi
    Pages 1-54
  3. Atsushi Yagi
    Pages 55-116
  4. Atsushi Yagi
    Pages 117-176
  5. Atsushi Yagi
    Pages 177-200
  6. Atsushi Yagi
    Pages 201-249
  7. Atsushi Yagi
    Pages 251-315
  8. Atsushi Yagi
    Pages 317-344
  9. Atsushi Yagi
    Pages 345-356
  10. Atsushi Yagi
    Pages 357-371
  11. Atsushi Yagi
    Pages 373-389
  12. Atsushi Yagi
    Pages 391-415
  13. Atsushi Yagi
    Pages 417-443
  14. Atsushi Yagi
    Pages 445-470
  15. Atsushi Yagi
    Pages 471-486
  16. Back Matter
    Pages 563-581

About this book

Introduction

The semigroup methods are known as a powerful tool for analyzing nonlinear diffusion equations and systems. The author has studied abstract parabolic evolution equations and their applications to nonlinear diffusion equations and systems for more than 30 years. He gives first, after reviewing the theory of analytic semigroups, an overview of the theories of linear, semilinear and quasilinear abstract parabolic evolution equations as well as general strategies for constructing dynamical systems, attractors and stable-unstable manifolds associated with those nonlinear evolution equations.

In the second half of the book, he shows how to apply the abstract results to various models in the real world focusing on various self-organization models: semiconductor model, activator-inhibitor model, B-Z reaction model, forest kinematic model, chemotaxis model, termite mound building model, phase transition model, and Lotka-Volterra competition model. The process and techniques are explained concretely in order to analyze nonlinear diffusion models by using the methods of abstract evolution equations.

Thus the present book fills the gaps of related titles that either treat only very theoretical examples of equations or introduce many interesting models from Biology and Ecology, but do not base analytical arguments upon rigorous mathematical theories.

Keywords

abstract parabolic evolution equations biological and ecological models biology dynamical systems ecology exponential attractors nonlinear diffusion systems numerical analysis

Authors and affiliations

  • Atsushi Yagi
    • 1
  1. 1.Graduate School of EngineeringOsaka UniversitySuita, OsakaJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-04631-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-04630-8
  • Online ISBN 978-3-642-04631-5
  • Series Print ISSN 1439-7382
  • About this book