Dispersive Partial Differential Equations: Wellposedness and Applications

by M. Burak Erdogan, Nikolaos Tzirakis

Overview

The area of nonlinear dispersive partial differential equations (PDEs) is a fast developing field which has become exceedingly technical in recent years. With this book, the authors provide a self-contained and accessible introduction for graduate or advanced undergraduate students in mathematics, engineering, and the physical sciences. Both classical and modern methods used in the field are described in detail, concentrating on the model cases that simplify the presentation without compromising the deep technical aspects of the theory, thus allowing students to learn the material in a short period of time. This book is appropriate both for self-study by students with a background in analysis, and for teaching a semester-long introductory graduate course in nonlinear dispersive PDEs. Copious exercises are included, and applications of the theory are also presented to connect dispersive PDEs with the more general areas of dynamical systems and mathematical physics.

Product Details

ISBN-13:	9781316694527
Publisher:	Cambridge University Press
Publication date:	05/03/2016
Series:	London Mathematical Society Student Texts , #86
Sold by:	Barnes & Noble
Format:	eBook
File size:	11 MB
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About the Author

M. Burak Erdoğan is a professor in the Department of Mathematics at the University of Illinois, Urbana-Champaign.
Nikolaos Tzirakis is an associate professor in the Department of Mathematics at the University of Illinois, Urbana-Champaign.

Table of Contents

Preface; Notation; 1. Preliminaries and tools; 2. Linear dispersive equations; 3. Methods for establishing wellposedness; 4. Global dynamics of nonlinear dispersive PDEs; 5. Applications of smoothing estimates; References; Index.

Editorial Reviews

'The exercises in each chapter, while not at all trivial, tremendously enhance one’s understanding of the material. The focus on periodic boundary conditions sets this book apart from related ones in the area, and yet the authors do a nice job discussing related well-posedness results and estimates on the real line as well. While certainly not meant for students without any analysis background, a thorough work-through of this book certainly brings one to the frontier of the theory of nonlinear dispersive PDEs.' Eric Stachura, MAA Reviews

'The book is a manual for beginning graduate students in the field of the general theory of nonlinear partial differential equations. The material is presented in the rigorous mathematical style, providing proofs of formal theorems, rather than less strict considerations which may be often encountered in physics literature.' Boris A. Malomed, Zentralblatt MATH

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