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Birkhäuser - Birkhäuser Mathematics | Nonlinear Partial Differential Equations - Asymptotic Behavior of Solutions and Self-Similar Solutions

Nonlinear Partial Differential Equations

Asymptotic Behavior of Solutions and Self-Similar Solutions

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

2010, XVIII, 294p. 7 illus..

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  • 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

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.

Content Level » Graduate

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;

Related subjects » Birkhäuser Mathematics

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