TY  - BOOK
AU  - Hayashi,Nakao
AU  - Kaikina,Elena
TI  - Nonlinear theory of pseudodifferential equations on a half-line
T2  - North Holland mathematics studies,
SN  - 9780444515698
AV  - QA377 .H393 2004eb
U1  - 515/.353 22
PY  - 2004///
CY  - Amsterdam, Boston
PB  - Elsevier
KW  - Evolution equations, Nonlinear
KW  - Pseudodifferential operators
KW  - fast
KW  - Electronic books
N1  - Includes bibliographical references and index; 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
N2  - 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
UR  - http://www.sciencedirect.com/science/book/9780444515698
UR  - http://www.sciencedirect.com/science/publication?issn=03040208&volume=194
ER  -