Dispersive and wave equations form an important class of equations. These include nonlinear equations and the wave maps equation. This introductory text describes the methods and results used ion modern analysis of the Cauchy problem. Working from his lectures at eh NSF-CBMS region conference at New Mexico U. in June 2005, Tao covers ordinary differential equations, constant coefficient linear dispersive equations, semilinear dispersive equations, the Korteweg de Vries equation, energy-critical semilinear dispersive equations and wave maps. Appendices include tools from harmonic analysis and material on the construction of ground states. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)
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Book by Terence Tao
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Condizione: Good. 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. Codice articolo 5573530
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Paperback. Condizione: Good-. Paperback in acceptable/good- condition. NOT ex-library. Text and math very good. Some wear/curl to corners, and some corners are creased. Spine deeply creased. 2022 reprint. Ships same or next business day from Dinkytown in Minneapolis, Minnesota. Codice articolo 324265
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Paperback. Condizione: New. 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. Codice articolo LU-9780821841433
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Paperback. Condizione: New. 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. Codice articolo LU-9780821841433
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