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Nonlinear Theory of Pseudodifferential Equations on a Half-line : Volume 194 - Nakao Hayashi

Nonlinear Theory of Pseudodifferential Equations on a Half-line

Volume 194

Hardcover Published: 27th January 2004
ISBN: 9780444515698
Number Of Pages: 340

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This book is the first attempt to develop systematically a general theory of the initial-boundary value problems for nonlinear evolution equations with pseudodifferential operators Ku on a half-line or on a segment. We study traditionally important problems, such as local and global existence of solutions and their properties, in particular much attention is drawn to the asymptotic behavior of solutions for large time. Up to now the theory of nonlinear initial-boundary value problems with a general pseudodifferential operator has not been well developed due to its difficulty. There are many open natural questions. Firstly how many boundary data should we pose on the initial-boundary value problems for its correct solvability? As far as we know there are few results in the case of nonlinear nonlocal equations. The methods developed in this book are applicable to a wide class of dispersive and dissipative nonlinear equations, both local and nonlocal.
-For the first time the definition of pseudodifferential operator on a half-line and a segment is done
-A wide class of nonlinear nonlocal and local equations is considered
-Developed theory is general and applicable to different equations
-The book is written clearly, many examples are considered
-Asymptotic formulas can be used for numerical computations by engineers and physicists
-The authors are recognized experts in the nonlinear wave phenomena

"The book is a first, very valuable contribution to the field, and should be recommended to everyone interested, and willing to go deeper into the subject (...)". Alberto Parmeggiani, Mathematical reviews, 2004.

Introduction
Preliminaries
Sobolev spaces
General Theory
Nonlinear Schrodinger Type Equations
Whitham Equation
Korteweg-de Vries-Burgers Equation
Large Initial Data
KdV-B Type Equation
Dirichlet Problem for KdV Equation
Neumann Problem for KdV Equation
Landau-Ginzburg Equation
Burgers Equation with Pumping
KdVB Equation on a Segment
NLS Equation on Segment
Periodic Problem
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780444515698
ISBN-10: 0444515690
Series: North-Holland Mathematics Studies
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 340
Published: 27th January 2004
Publisher: Elsevier Science & Technology
Country of Publication: GB
Dimensions (cm): 24.0 x 16.5  x 1.52
Weight (kg): 0.66