Introduction to Nonlinear Dispersive Equations (Universitext) - Tapa blanda

Libro 72 de 261: Universitext

Linares, Felipe; Ponce, Gustavo

 
9781493921805: Introduction to Nonlinear Dispersive Equations (Universitext)
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ISBN 10: 1493921800 ISBN 13: 9781493921805
Editorial: Springer, 2014

Sinopsis

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.

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Acerca del 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.

De la contraportada

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.

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Editorial
Springer
Año de publicación
2014
Idioma
Inglés
ISBN 10 
1493921800
ISBN 13 
9781493921805
Encuadernación
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Número de edición
2
Número de páginas
316
Contacto del fabricante
no disponible
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Otras ediciones populares con el mismo título

9780387848983: Introduction to Nonlinear Dispersive Equations (Universitext)

Edición Destacada

ISBN 10:  0387848983 ISBN 13:  9780387848983
Editorial: Springer, 2010
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