Nonlinear Partial Differential Equations Asymptotic Behavior of Solutions and Self-Similar Solutions /

• Main Authors: Giga, Mi-Ho. (Author), Giga, Yoshikazu. (Author), Saal, J<U+00fc>rgen. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston : Birkhũser Boston, 2010.
• Series: Progress in Nonlinear Differential Equations and Their Applications ; 79
• Subjects: Mathematics.; Global analysis (Mathematics).; Functional analysis.; Differential equations, partial.; Partial Differential Equations.; Functional Analysis.; Analysis.; Approximations and Expansions.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-4651-6

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...

Table of Contents:

• Preface
• Part I Asymptotic Behavior of Solutions of Partial Differential Equations
• 1 Behavior Near Time Infinity of Solutions of the Heat Equation
• 2 Behavior Near Time Infinity of Solutions of the Vorticity Equations
• 3 Self-Similar Solutions for Various Equations
• Part II Useful Analytic Tools
• 4 Various Properties of Solutions of the Heat Equation
• 5 Compactness Theorems
• 6 Calculus Inequalities
• 7 Convergence Theorems in the Theory of Integration
• Answers to Exercises
• Comments on Further References
• References
• Glossary
• Index.