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Introduction to Nonlinear Dispersive Equations
Taschenbuch von Gustavo Ponce (u. a.)
Sprache: Englisch

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Beschreibung
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 material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg¿de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research.
Thesecond edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers to enter this actively developing field.
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 material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg¿de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research.
Thesecond edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers to enter this actively developing field.
Über den Autor

Felipe Linares is a Researcher at the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil.

Gustavo Ponce is a Professor of Mathematics at the University of California in Santa Barbara.

Zusammenfassung

Includes a nice selection of topics

Contains a large section of non-standard exercises

Offers accessible presentation of key tools in harmonic and Fourier analysis

Includes supplementary material: [...]

Inhaltsverzeichnis
1. The Fourier Transform.- 2. Interpolation of Operators.- 3. Sobolev Spaces and Pseudo-Differential Operators.- 4. The Linear Schrodinger Equation.- 5. The Non-Linear Schrodinger Equation.- 6. Asymptotic Behavior for NLS Equation.- 7. Korteweg-de Vries Equation.- 8. Asymptotic Behavior for k-gKdV Equations.- 9. Other Nonlinear Dispersive Models.- 10. General Quasilinear Schrodinger Equation.- Proof of Theorem 2.8.- Proof of Lemma 4.2.- References.- Index.
Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 316
Reihe: Universitext
Inhalt: xiv
301 S.
1 s/w Illustr.
301 p. 1 illus.
ISBN-13: 9781493921805
ISBN-10: 1493921800
Sprache: Englisch
Herstellernummer: 86374587
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Ponce, Gustavo
Linares, Felipe
Auflage: 2nd ed. 2015
Hersteller: Springer US
Springer New York
Universitext
Maße: 235 x 155 x 18 mm
Von/Mit: Gustavo Ponce (u. a.)
Erscheinungsdatum: 15.12.2014
Gewicht: 0,482 kg
preigu-id: 105091935
Über den Autor

Felipe Linares is a Researcher at the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil.

Gustavo Ponce is a Professor of Mathematics at the University of California in Santa Barbara.

Zusammenfassung

Includes a nice selection of topics

Contains a large section of non-standard exercises

Offers accessible presentation of key tools in harmonic and Fourier analysis

Includes supplementary material: [...]

Inhaltsverzeichnis
1. The Fourier Transform.- 2. Interpolation of Operators.- 3. Sobolev Spaces and Pseudo-Differential Operators.- 4. The Linear Schrodinger Equation.- 5. The Non-Linear Schrodinger Equation.- 6. Asymptotic Behavior for NLS Equation.- 7. Korteweg-de Vries Equation.- 8. Asymptotic Behavior for k-gKdV Equations.- 9. Other Nonlinear Dispersive Models.- 10. General Quasilinear Schrodinger Equation.- Proof of Theorem 2.8.- Proof of Lemma 4.2.- References.- Index.
Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 316
Reihe: Universitext
Inhalt: xiv
301 S.
1 s/w Illustr.
301 p. 1 illus.
ISBN-13: 9781493921805
ISBN-10: 1493921800
Sprache: Englisch
Herstellernummer: 86374587
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Ponce, Gustavo
Linares, Felipe
Auflage: 2nd ed. 2015
Hersteller: Springer US
Springer New York
Universitext
Maße: 235 x 155 x 18 mm
Von/Mit: Gustavo Ponce (u. a.)
Erscheinungsdatum: 15.12.2014
Gewicht: 0,482 kg
preigu-id: 105091935
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