Introduction to nonlinear dispersive equations

✍ Scribed by Gustavo Ponce, Felipe Linares (auth.)

Publisher: Springer New York
Year: 2009
Tongue: English
Leaves: 263
Series: Universitext
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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 Contents

Front Matter....Pages 1-9
The Fourier Transform....Pages 1-24
Interpolation of Operators. A Multiplier Theorem....Pages 1-19
Sobolev Spaces and Pseudo-Differential Operators....Pages 1-14
The Linear Schrodinger Equation....Pages 1-29
The Nonlinear Schrodinger Equation. Local Theory....Pages 1-29
Asymptotic Behavior for NLS Equation....Pages 1-20
Korteweg-de Vries Equation....Pages 1-34
Asymptotic Behavior for k-gKdV Equations....Pages 1-17
Other Nonlinear Dispersive Models....Pages 1-20
General Quasilinear Schrodinger Equation....Pages 1-21
Back Matter....Pages 1-26

✦ Subjects

Partial Differential Equations

📜 SIMILAR VOLUMES

Introduction to Nonlinear Dispersive Equ

📁 Introduction to Nonlinear Dispersive Equations

✍ Gustavo Ponce, Felipe Linares (auth.) 📂 Library 📅 2009 🏛 Springer New York 🌐 English

<P>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

Introduction to Nonlinear Dispersive Equ

📁 Introduction to Nonlinear Dispersive Equations

✍ Felipe Linares, Gustavo Ponce (auth.) 📂 Library 📅 2015 🏛 Springer-Verlag New York 🌐 English

<p><p>This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of backgrou

Introduction to Nonlinear Dispersive Equ

📁 Introduction to Nonlinear Dispersive Equations

✍ Felipe Linares, Gustavo Ponce 📂 Library 📅 2014 🏛 Springer 🌐 English

<p>This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background

Nonlinear dispersive equations

📁 Nonlinear dispersive equations

✍ Jaime Angulo Pava 📂 Library 📅 2009 🏛 American Mathematical Society 🌐 English

This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications a

Lectures on Nonlinear Dispersive Equatio

📁 Lectures on Nonlinear Dispersive Equations

✍ Ozawa T., Tsutsumi Y. (eds.) 📂 Library 📅 2004 🌐 English

This volume, together with the next, is intended as the proceedings of expository lectures in Special Months "Nonlinear Dispersive Equations". Nonlinear dispersive equations, such as nonlinear Schrodinger equations, KdV equation, and Benjamin-Ono equation, are of mathematical and physical importance

Lectures on Nonlinear Dispersive Equatio

📁 Lectures on Nonlinear Dispersive Equations

✍ Ozawa T., Tsutsumi Y. (eds.) 📂 Library 📅 2004 🌐 English