Nonlinear theory of pseudodifferential equations on a half-line [electronic resource] / Nakao Hayashi and Elena Kaikina.

By: Hayashi, NakaoContributor(s): Kaikina, ElenaMaterial type: Text

TextSeries: North-Holland mathematics studies ; 194.Publication details: Amsterdam ; Boston : Elsevier, 2004. Edition: 1st edDescription: 1 online resource (xix, 340 p.)ISBN: 9780444515698; 0444515690Subject(s): Evolution equations, Nonlinear | Pseudodifferential operators | Evolution equations, Nonlinear | Pseudodifferential operatorsGenre/Form: Electronic books.Additional physical formats: Print version:: Nonlinear theory of pseudodifferential equations on a half-line.DDC classification: 515/.353 LOC classification: QA377 | .H393 2004ebOnline resources: ScienceDirect | Volltext

Contents:

Introduction -- 1 Preliminaries -- 2 Sobolev spaces -- 3 General Theory -- 4 Nonlinear Schrodinger Type Equations -- 5 Whitham Equation -- 6 Korteweg-de Vries-Burgers Equation -- 7 Large Initial Data -- 8 KdV-B Type Equation -- 9 Dirichlet Problem for KdV Equation -- 10 Neumann Problem for KdV Equation -- 11 Landau-Ginzburg Equations -- 12 Burgers Equation with Pumping -- 13 KdVB Equation on a Segment -- 14 NLS Equation on Segment -- 15 Periodic Problem -- Bibliography -- Index.

Summary: 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.

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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.

Includes bibliographical references and index.

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