Local And Global Analysis of Nonlinear Dispersive And Wave Equations (CBMS Regional Conference Series in Mathematics) by Terence Tao (PDF)

Description

Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrödinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation. This book is an introduction to the methods and results used in the modern analysis (both locally and globally in time) of the Cauchy problem for such equations. Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems. As the subject is vast, the book does not attempt to give a comprehensive survey of the field, but instead concentrates on a representative sample of results for a selected set of equations, ranging from the fundamental local and global existence theorems to very recent results, particularly focusing on the recent progress in understanding the evolution of energy-critical dispersive equations from large data. The book is suitable for a graduate course on nonlinear PDE. Readership Graduate students and research mathematicians interested in nonlinear partial differential equations.

User’s Reviews

Editorial Reviews: Review The work is well suited for a graduate level course on nonlinear PDE, and it is to be thoroughly recommended. — –Alan Jeffrey for Zentralblatt MATHTao certainly succeeds in writing a vivid and instructional text on nonlinear dispersive partial differential equations. It touches on topics of recent research interest and is a valuable source both for the beginning graduate student and, to some extent, for the advanced researcher. –Mathematical Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excellent book for the beginners to have a general idea of the dispersive wave equations!

⭐I love it extremely.

⭐El contenido del libro está excelente. La calidad (por el precio) y por el contenido intelectual no tienen ningún problema; el problema es con las condiciones en que transportan los libros (es obvio quién es el responsable de eso). Por eso le doy sólo una estrella: más seriedad con su negocio señores, nada es para siempre.The best book about dispersive PDEs.With Tao, everything is clear and obvious. It is a pleasure to read such a book. It is comprehensive, a lot of physical aspects are also developped. I focused on the part on Schrodinger’s equation which is very clear.The part on Bourgain spaces is, in my mind, the best introduction ever on X^{s,b} spaces.

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