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OverviewThe aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way. The first three chapters are dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev spaces. The authors then proceed to use the linear Schrodinger equation to describe properties enjoyed by general dispersive equations. This information is then used to treat local and global well-posedness for the semi-linear Schrodinger equations. The end of each chapter contains recent developments and open problems, as well as exercises. Full Product DetailsAuthor: Felipe Linares , Gustavo PoncePublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Dimensions: Width: 15.60cm , Height: 1.40cm , Length: 23.40cm Weight: 0.391kg ISBN: 9780387848983ISBN 10: 0387848983 Pages: 260 Publication Date: 01 December 2008 Audience: College/higher education , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Unknown Availability: In Print  Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock. Table of ContentsThe Fourier Transform.- Interpolation of Operators. A Multiplier Theorem.- Sobolev Spaces and Pseudo-Differential Operators.- The Linear Schrodinger Equation.- The Nonlinear Schrodinger Equation. Local Theory.- Asymptotic Behavior for NLS Equation.- Korteweg-de Vries Equation.- Asymptotic Behavior for k-gKdV Equations.- Other Nonlinear Dispersive Models.- General Quasilinear Schrodinger Equation.ReviewsFrom the reviews: This monograph gives a quick introduction to the modern harmonic analysis of nonlinear dispersive equations, with a particular emphasis on the nonlinear Schrodinger and Korteweg-de Vries equations. The monograph can be used for a specialized graduate course or for independent reading. It deals with complicated problems of analysis in an easy way, which makes reading of this book to be pleasant and informative. Many examples are described as illustrations of the theorems and as the end-of-chapter exercises. (Dmitry Pelinovsky, Zentralblatt MATH, Vol. 1178, 2010) From the reviews: This monograph gives a quick introduction to the modern harmonic analysis of nonlinear dispersive equations, with a particular emphasis on the nonlinear Schrodinger and Korteweg-de Vries equations. The monograph can be used for a specialized graduate course or for independent reading. It deals with complicated problems of analysis in an easy way, which makes reading of this book to be pleasant and informative. Many examples are described as illustrations of the theorems and as the end-of-chapter exercises. (Dmitry Pelinovsky, Zentralblatt MATH, Vol. 1178, 2010) This text contains an up-to-date account of results and methods in the well-posedness theory for initial-value problems of nonlinear dispersive equations. ... using only this text, a reader who has had one year of graduate analysis should be able to follow the proofs to completion without much difficulty. ... the book contains several extended sections comprising guides to the history of the subject and the state of current knowledge. (John Albert, Mathematical Reviews, Issue 2010 j) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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