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# Nonlinear Theory of Pseudodifferential Equations on a Half-line

- 1st Edition, Volume 194 - January 13, 2004
- Authors: Nakao Hayashi, Elena Kaikina
- Language: English
- Hardback ISBN:9 7 8 - 0 - 4 4 4 - 5 1 5 6 9 - 8
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 5 3 7 6 1 - 0

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… Read more

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Request a sales quoteThis 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

Mathematicians, Physicists, Engineers and graduate students.

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

- No. of pages: 340
- Language: English
- Edition: 1
- Volume: 194
- Published: January 13, 2004
- Imprint: Elsevier Science
- Hardback ISBN: 9780444515698
- eBook ISBN: 9780080537610

NH

### Nakao Hayashi

Affiliations and expertise

Osaka University, JapanEK

### Elena Kaikina

Affiliations and expertise

Technological Institute of Morelia, Mexico.