Nonlinear Theory of Pseudodifferential Equations on a Half-Line: Volume 194

ISBN-13: 9780444515698 / Angielski / Twarda / 2004 / 340 str.

Nakao Hayashi; Elena Kaikina; Jan Van Mill

Opis

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

Recenzje

"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.

Spis treści

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