Nonlinear Partial Differential Equations

Asymptotic Behavior of Solutions and Self-Similar Solutions

  • Mi-Ho Giga
  • Yoshikazu Giga
  • Jürgen Saal

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 79)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Asymptotic Behavior of Solutions of Partial Differential Equations

    1. Front Matter
      Pages 1-1
    2. Mi-Ho Giga, Yoshikazu Giga, Jürgen Saal
      Pages 3-36
    3. Mi-Ho Giga, Yoshikazu Giga, Jürgen Saal
      Pages 37-103
    4. Mi-Ho Giga, Yoshikazu Giga, Jürgen Saal
      Pages 105-138
  3. Useful Analytic Tools

    1. Front Matter
      Pages 140-140
    2. Mi-Ho Giga, Yoshikazu Giga, Jürgen Saal
      Pages 141-180
    3. Mi-Ho Giga, Yoshikazu Giga, Jürgen Saal
      Pages 181-188
    4. Mi-Ho Giga, Yoshikazu Giga, Jürgen Saal
      Pages 189-238
    5. Mi-Ho Giga, Yoshikazu Giga, Jürgen Saal
      Pages 239-247
  4. Back Matter
    Pages 249-294

About this book

Introduction

The main focus of this textbook, in two parts, is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The exposition moves systematically from the basic to more sophisticated concepts with recent developments and several open problems.  With challenging exercises, examples, and illustrations to help explain the rigorous analytic basis for the Navier–-Stokes equations, mean curvature flow equations, and other important equations describing real phenomena, this book is written for graduate students and researchers, not only in mathematics but also in other disciplines.

Nonlinear Partial Differential Equations will serve as an excellent textbook for a first course in modern analysis or as a useful self-study guide. Key topics in nonlinear partial differential equations as well as several fundamental tools and methods are presented.  The only prerequisite required is a basic course in calculus.

Keywords

Burgers vortex Navier-Stokes equations asymptotic behavior calculus calculus inequalities compactness differential equation mean curvature flow mean curvature flow equations nonlinear functional analysis nonlinear partial differential equations;

Authors and affiliations

  • Mi-Ho Giga
    • 1
  • Yoshikazu Giga
    • 2
  • Jürgen Saal
    • 3
  1. 1., Graduate School of Mathematical SciencesUniversity of TokyoMeguro-kuJapan
  2. 2.Graduate School of, Mathematical SciencesUniversity of TokyoTokyoJapan
  3. 3., Center of Smart InterfacesTechnische Universität DarmstadtDarmstadtGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4651-6
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4173-3
  • Online ISBN 978-0-8176-4651-6
  • About this book