Progress in Nonlinear Differential Equations and Their Applications

Nonlinear Partial Differential Equations

Asymptotic Behavior of Solutions and Self-Similar Solutions

Authors: Giga, Mi-Ho, Giga, Yoshikazu, Saal, Jürgen

  • Challenges the reader with many exercises, examples and illustrations
  • Includes recent developments and several open problems
  • Serves as an excellent textbook for a first course in modern analysis or as an excellent resource for a self-study guide
  • Key topics in nonlinear partial differential equations as well as several fundamental tools and methods are presented
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Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-0-8176-4651-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.95
price for USA
  • ISBN 978-0-8176-4173-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

Reviews

From the reviews:

“This book studies the asymptotic behavior of solutions to some nonlinear evolution problems by using rescaling … methods with self-similar solutions … . not only are there exercises but also answers to these exercises. In any case this book is a very welcome and useful addition to the literature.” (Jesús Hernández, Mathematical Reviews, Issue 2011 f)

“The book presents typical methods … for the examination of the behavior of solutions of nonlinear partial differential equations of diffusion type. … The aim of the authors was to teach the readers to deal with such tools during the study of PDEs and to give them a strong motivation for their study. … The book is written in a very pedagogical way. Each chapter contains plenty of exercises whose detailed solutions can be found at the end of the book.” (Pavol Quittner, Zentralblatt MATH, Vol. 1215, 2011)


Table of contents (7 chapters)

  • Behavior Near Time Infinity of Solutions of the Heat Equation

    Giga, Mi-Ho (et al.)

    Pages 3-36

  • Behavior Near Time Infinity of Solutions of the Vorticity Equations

    Giga, Mi-Ho (et al.)

    Pages 37-103

  • Self-Similar Solutions for Various Equations

    Giga, Mi-Ho (et al.)

    Pages 105-138

  • Various Properties of Solutions of the Heat Equation

    Giga, Mi-Ho (et al.)

    Pages 141-180

  • Compactness Theorems

    Giga, Mi-Ho (et al.)

    Pages 181-188

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-0-8176-4651-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.95
price for USA
  • ISBN 978-0-8176-4173-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Partial Differential Equations
Book Subtitle
Asymptotic Behavior of Solutions and Self-Similar Solutions
Authors
Series Title
Progress in Nonlinear Differential Equations and Their Applications
Series Volume
79
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-8176-4651-6
DOI
10.1007/978-0-8176-4651-6
Hardcover ISBN
978-0-8176-4173-3
Series ISSN
1421-1750
Edition Number
1
Number of Pages
XVIII, 294
Number of Illustrations and Tables
7 b/w illustrations
Topics