03294nam a22005055i 4500 978-0-8176-4651-6 DE-He213 20260521092029.0 cr nn 008mamaa 100601s2010 xxu| s |||| 0|eng d 9780817646516 99780817646516 10.1007/978-0-8176-4651-6 doi 515.353 23 Giga, Mi-Ho. author. Nonlinear Partial Differential Equations [electronic resource] : Asymptotic Behavior of Solutions and Self-Similar Solutions / by Mi-Ho Giga, Yoshikazu Giga, Jürgen Saal. Boston : Birkhäuser Boston, 2010. XVIII, 294p. 7 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Progress in Nonlinear Differential Equations and Their Applications ; 79 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. MATHEMATICS. GLOBAL ANALYSIS (MATHEMATICS). FUNCTIONAL ANALYSIS. DIFFERENTIAL EQUATIONS, PARTIAL. MATHEMATICS. PARTIAL DIFFERENTIAL EQUATIONS. FUNCTIONAL ANALYSIS. ANALYSIS. APPROXIMATIONS AND EXPANSIONS. Giga, Yoshikazu. author. Saal, Jürgen. author. SpringerLink (Online service) Springer eBooks Printed edition: 9780817641733 Progress in Nonlinear Differential Equations and Their Applications ; 79 http://dx.doi.org/10.1007/978-0-8176-4651-6 Ver el texto completo en las instalaciones del CICY ZDB-2-SMA ddc ER 35676 35676 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 515.353 2025-10-06 08:44:38 2025-10-06 ER