Introduction to Nonlinear Dispersive Equations [electronic resource] /
Linares, Felipe.author.
Ponce, Gustavo.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
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.
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.
Partial differential equations.
Partial Differential Equations.
Universitext