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Introduction to Nonlinear Dispersive Equations [electronic resource] / by Gustavo Ponce, Felipe Linares.

By: Ponce, Gustavo [author.].
Contributor(s): Linares, Felipe [author.] | SpringerLink (Online service).
Material type: TextTextSeries: Universitext: Publisher: New York, NY : Springer New York, 2009Description: XII, 260 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780387848990.Subject(s): Differential equations, partial | Partial Differential EquationsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 515.353 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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Item type Current location Call number Status Date due Barcode Item holds
E-BOOKS E-BOOKS ISI Library, Kolkata
 
Available EB1631
Total holds: 0

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.

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