Nonlinear Theory of Pseudodifferential Equations on a Half-line, Volume 194

1st Edition

Authors: Nakao Hayashi Elena Kaikina
Print ISBN: 9780444515698
eBook ISBN: 9780080537610
Imprint: Elsevier Science
Published Date: 13th January 2004
Page Count: 340

Institutional Access


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.

Key Features

· 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


Mathematicians, Physicists, Engineers and graduate students.

Table of 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


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© Elsevier Science 2004
Elsevier Science
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About the Author

Nakao Hayashi

Affiliations and Expertise

Osaka University, Japan

Elena Kaikina

Affiliations and Expertise

Technological Institute of Morelia, Mexico.


"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.