Introduction to Nonlinear Dispersive Equations
Wydawnictwo: Springer Verlag
* Contains a large section of non-standard exercises
* Offers accessible presentation of key tools in harmonic and Fourier analysis
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.Table of contentsPreface.- The Fourier Transform.- Interpolation of Operators: A Multiplier Theorem.- Sobolev Spaces and Pseudo-differential Operators.- The Linear Schrödinger Equation.- The Nonlinear Schrödinger Equation, Local theory.- Asymptotic Behavior for NLS Equation.- Korteweg-de Vries Equation.- Asymptotic Behavior of Solutions for the k-gKdV Equations.- Other Nonlinear Dispersive Models.- General Quasilinear Schrödinger Equation.- Appendix.- References.- Index.