Nonlinear Dispersive Equations: Local and Global Analysis (Volume 106)

Tao, Terence

ISBN 10: 0821841432 / ISBN 13: 9780821841433

Published by American Mathematical Society, 2006

About this Item

Volume 106. This is an ex-library book and may have the usual library/used-book markings inside.This book has soft covers. In good all round condition. Library sticker on front cover. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,800grams, ISBN:9780821841433.

Seller Inventory # 5573530

Bibliographic Details

• Title: Nonlinear Dispersive Equations: Local and Global Analysis (Volume 106)
• Publisher: American Mathematical Society
• Publication Date: 2006
• Language: English
• ISBN 10: 0821841432
• ISBN 13: 9780821841433
• Binding: Soft cover
• Condition: Good
• Seller catalogs:
  • Mathematics

About this title

Synopsis

Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrodinger 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.

About the Author

Terence Tao was the winner of the 2014 Breakthrough Prize in Mathematics. He is the James and Carol Collins Chair of mathematics at UCLA and the youngest person ever to be promoted to full professor at the age of 24. In 2006 Tao became the youngest ever mathematician to win the Fields Medal. His other honours include the George Polya Prize from the Society for Industrial and Applied Mathematics (2010), the Alan T Waterman Award from the National Science Foundation (2008), the SASTRA Ramanujan Prize (2006), the Clay Research Award from the Clay Mathematical Institute (2003), the Bocher Memorial Prize from the American Mathematical Society (2002) and the Salem Prize (2000).