Dispersive Partial Differential Equations: Wellposedness and Applications

ISBN-13: 9781316602935 / Angielski / Miękka / 2016 / 197 str.

M. Burak Erdogan;Nikoloas Tzirakis

Opis

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.

Recenzje

'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

Spis treści

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.