Buchcover - Introduction to Nonlinear Dispersive Equations - ISBN 978-0-387-84899-0
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 Schrödinger 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)
The 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.
