Introduction to Nonlinear Dispersive Equations
Ponce, Gustavo.
creator
author.
aut
http://id.loc.gov/vocabulary/relators/aut
Linares, Felipe.
author.
aut
http://id.loc.gov/vocabulary/relators/aut
SpringerLink (Online service)
text
xxu
2009
monographic
eng
access
XII, 260 p. online resource.
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.
The Fourier Transform -- Interpolation of Operators. A Multiplier Theorem -- Sobolev Spaces and Pseudo-Differential Operators -- The Linear Schrodinger Equation -- The Nonlinear Schrodinger Equation. Local Theory -- Asymptotic Behavior for NLS Equation -- Korteweg-de Vries Equation -- Asymptotic Behavior for k-gKdV Equations -- Other Nonlinear Dispersive Models -- General Quasilinear Schrodinger Equation.
by Gustavo Ponce, Felipe Linares.
Differential equations, partial
Partial Differential Equations
QA370-380
515.353
Springer eBooks
Universitext
9780387848990
https://doi.org/10.1007/978-0-387-84899-0
https://doi.org/10.1007/978-0-387-84899-0
ISI Library, Kolkata
100301
20181204133152.0
978-0-387-84899-0