TY - BOOK
AU - Ponce,Gustavo
AU - Linares,Felipe
ED - SpringerLink (Online service)
TI - Introduction to Nonlinear Dispersive Equations
T2 - Universitext,
SN - 9780387848990
AV - QA370-380
U1 - 515.353 23
PY - 2009///
CY - New York, NY
PB - Springer New York
KW - Differential equations, partial
KW - Partial Differential Equations
N1 - 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
N2 - 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
UR - https://doi.org/10.1007/978-0-387-84899-0
ER -