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Abstract Parabolic Evolution Equations and their Applications

  • Book
  • © 2010

Overview

Authors:
  1. Atsushi Yagi

    1. Graduate School of Engineering, Osaka University, Suita, Osaka, Japan

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  • Fills the gaps of existing literature
  • Presents rigorous mathematical theories
  • Applies results focusing on various self-organization models
  • Author has studied abstract parabolic evolution equations and their applications to nonlinear diffusion equations and systems for more than 30 years
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XVIII
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  2. Preliminaries

    • Atsushi Yagi
    Pages 1-54

  3. Sectorial Operators

    • Atsushi Yagi
    Pages 55-116

  4. Linear Evolution Equations

    • Atsushi Yagi
    Pages 117-176

  5. Semilinear Evolution Equations

    • Atsushi Yagi
    Pages 177-200

  6. Quasilinear Evolution Equations

    • Atsushi Yagi
    Pages 201-249

  7. Dynamical Systems

    • Atsushi Yagi
    Pages 251-315

  8. Numerical Analysis

    • Atsushi Yagi
    Pages 317-344

  9. Semiconductor Models

    • Atsushi Yagi
    Pages 345-356

  10. Activator–Inhibitor Models

    • Atsushi Yagi
    Pages 357-371

  11. Belousov–Zhabotinskii Reaction Models

    • Atsushi Yagi
    Pages 373-389

  12. Forest Kinematic Model

    • Atsushi Yagi
    Pages 391-415

  13. Chemotaxis Models

    • Atsushi Yagi
    Pages 417-443

  14. Termite Mound Building Model

    • Atsushi Yagi
    Pages 445-470

  15. Adsorbate-Induced Phase Transition Model

    • Atsushi Yagi
    Pages 471-486

  16. Lotka–Volterra Competition Model with Cross-Diffusion

    • Atsushi Yagi
    Pages 487-526

  17. Characterization of Domains of Fractional Powers

    • Atsushi Yagi
    Pages 527-562

  18. Back Matter

    Pages 563-581
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Keywords

About this book

This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0

Authors and Affiliations

  • Graduate School of Engineering, Osaka University, Suita, Osaka, Japan

    Atsushi Yagi

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