Asymptotic Behavior of Solutions and Self-Similar Solutions Giga, Mi-Ho. creator author. Giga, Yoshikazu. author. Saal, Jürgen. author. SpringerLink (Online service) text xxu 2010 monographic eng

electronic

electronic resource

access XVIII, 294p. 7 illus. online resource. 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. 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. by Mi-Ho Giga, Yoshikazu Giga, Jürgen Saal. MATHEMATICS GLOBAL ANALYSIS (MATHEMATICS) FUNCTIONAL ANALYSIS DIFFERENTIAL EQUATIONS, PARTIAL MATHEMATICS PARTIAL DIFFERENTIAL EQUATIONS FUNCTIONAL ANALYSIS ANALYSIS APPROXIMATIONS AND EXPANSIONS 515.353 9780817646516 99780817646516 http://dx.doi.org/10.1007/978-0-8176-4651-6 http://dx.doi.org/10.1007/978-0-8176-4651-6 100601 20260521092029.0 978-0-8176-4651-6