Nonlinear Dispersive Equations: Local and Global Analysis by Terence Tao (Paperback, 2006)
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- DescriptionAmong nlinear PDEs, dispersive and wave equations form an important class of equations. These include the nlinear Schrodinger equation, the nlinear 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 kwledge of graduate real analysis and Fourier analysis, the text first presents basic nlinear tools such as the bootstrap method and perturbation theory in the simpler context of nlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE.These methods are then combined to study four model nlinear 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 t 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 nlinear PDE.
- Author BiographyTerence 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).
- Author(s)Terence Tao
- PublisherAmerican Mathematical Society
- Date of Publication15/06/2006
- SubjectScience & Mathematics: Textbooks & Study Guides
- Series TitleCBMS Regional Conference Series in Mathematics
- Series Part/Volume NumberNo. 106
- Place of PublicationProvidence
- Country of PublicationUnited States
- ImprintAmerican Mathematical Society
- Content NoteIllustrations
- Weight675 g
- Spine20 mm
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