Nonlinear theory of pseudodifferential equations on a half-line
著者
書誌事項
Nonlinear theory of pseudodifferential equations on a half-line
（North-Holland mathematics studies, 194）
Elsevier, 2004
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注記
Bibliography: p. 309-315
Includes index
内容説明・目次
内容説明
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.
目次
Introduction1 Preliminaries2 Sobolev spaces3 General Theory4 Nonlinear Schrodinger Type Equations5 Whitham Equation6 Korteweg-de Vries-Burgers Equation7 Large Initial Data8 KdV-B Type Equation9 Dirichlet Problem for KdV Equation10 Neumann Problem for KdV Equation11 Landau-Ginzburg Equations12 Burgers Equation with Pumping13 KdVB Equation on a Segment14 NLS Equation on Segment15 Periodic ProblemBibliographyIndex
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