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＜電子ブック＞
Nonlinear Partial Differential Equations : Asymptotic Behavior of Solutions and Self-Similar Solutions / by Mi-Ho Giga, Yoshikazu Giga, Jürgen Saal
(Progress in Nonlinear Differential Equations and Their Applications. ISSN:23740280 ; 79)

版	1st ed. 2010.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2010
本文言語	英語
大きさ	XVIII, 294 p. 7 illus : online resource
著者標目	*Giga, Mi-Ho author Giga, Yoshikazu author Saal, Jürgen author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Functional analysis LCSH:Mathematical analysis LCSH:Approximation theory FREE:Differential Equations FREE:Functional Analysis FREE:Analysis FREE:Approximations and Expansions
一般注記	Asymptotic Behavior of Solutions of Partial Differential Equations -- Behavior Near Time Infinity of Solutions of the Heat Equation -- Behavior Near Time Infinity of Solutions of the Vorticity Equations -- Self-Similar Solutions for Various Equations -- Useful Analytic Tools -- Various Properties of Solutions of the Heat Equation -- Compactness Theorems -- Calculus Inequalities -- Convergence Theorems in the Theory of Integration 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 HTTP:URL=https://doi.org/10.1007/978-0-8176-4651-6

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