E-Book, Englisch, 260 Seiten
Reihe: Universitext
Linares / Ponce Introduction to Nonlinear Dispersive Equations
1. Auflage 2009
ISBN: 978-0-387-84899-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 260 Seiten
Reihe: Universitext
ISBN: 978-0-387-84899-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Autoren/Hrsg.
Weitere Infos & Material
1;Preface;5
2;Contents;8
3;The Fourier Transform;11
4;Interpolation of Operators. A Multiplier Theorem;35
5;An Introduction to Sobolev Spaces and Pseudo- differential Operators;54
6;The Linear Schr ödinger Equation;68
7;The Nonlinear Schrödinger Equation. Local Theory;97
8;Asymptotic Behavior of Solutions for the NLS Equation;126
9;Korteweg-de Vries Equation;146
10;Asymptotic Behavior of Solutions for the k- gKdV Equations;180
11;Other Nonlinear Dispersive Models;197
12;General Quasilinear Schr ödinger Equation;217
13;Appendix;238
14;References;243
15;Index;258
