Introduction to Nonlinear Dispersive Equations (Universitext)

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9781493921805: Introduction to Nonlinear Dispersive Equations (Universitext)

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.

The second 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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

About the Author :

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.

Review :

“This is the second edition of a self-contained graduate level introduction to the results and methods in the well-posedness theory for initial-value problems of nonlinear dispersive equations with special focus on the nonlinear Schrödinger and Korteweg de Vries equations. ... I strongly welcome this updated version and I can only recommend it warmly to anybody (both students and teachers) interested in this central area of analysis.” (G. Teschl, Monatshefte für Mathematik, Vol. 180, 2016)

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

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Felipe Linares, Gustavo Ponce
Edité par Springer-Verlag New York Inc., United States (2015)
ISBN 10 : 1493921800 ISBN 13 : 9781493921805
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Description du livre Springer-Verlag New York Inc., United States, 2015. Paperback. État : New. 2nd Revised edition. Language: English . Brand New Book. 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 Schrodinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrodinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrodinger 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 Schrodinger equation, taking the reader to the forefront of recent research.The second 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. N° de réf. du libraire AAU9781493921805

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Felipe Linares, Gustavo Ponce
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ISBN 10 : 1493921800 ISBN 13 : 9781493921805
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Description du livre Springer New York 2014-12-15, New York, NY, 2014. paperback. État : New. N° de réf. du libraire 9781493921805

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Description du livre Springer-Verlag New York Inc. Paperback. État : new. BRAND NEW, Introduction to Nonlinear Dispersive Equations: 2015 (2nd Revised edition), Felipe Linares, Gustavo Ponce, 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 Schrodinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrodinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrodinger 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 Schrodinger equation, taking the reader to the forefront of recent research. The second 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. N° de réf. du libraire B9781493921805

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Felipe Linares, Gustavo Ponce
Edité par Springer-Verlag New York Inc., United States (2015)
ISBN 10 : 1493921800 ISBN 13 : 9781493921805
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Description du livre Springer-Verlag New York Inc., United States, 2015. Paperback. État : New. 2nd ed. 2015. Language: English . Brand New Book. 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 Schrodinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrodinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrodinger 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 Schrodinger equation, taking the reader to the forefront of recent research.The second 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. N° de réf. du libraire AAU9781493921805

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Description du livre Springer, 2014. État : New. Introduction to Nonlinear Dispersive Equations Series: Universitext. Num Pages: 301 pages, 1 black & white illustrations, 2 black & white tables, biography. BIC Classification: PBKJ. Category: (G) General (US: Trade). Dimension: 159 x 232 x 17. Weight in Grams: 474. . 2014. 2nd ed. 2015. Paperback. . . . . . N° de réf. du libraire V9781493921805

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Description du livre Springer. État : New. Introduction to Nonlinear Dispersive Equations Series: Universitext. Num Pages: 301 pages, 1 black & white illustrations, 2 black & white tables, biography. BIC Classification: PBKJ. Category: (G) General (US: Trade). Dimension: 159 x 232 x 17. Weight in Grams: 474. . 2014. 2nd ed. 2015. Paperback. . . . . Books ship from the US and Ireland. N° de réf. du libraire V9781493921805

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