Nonlinear Theory of Pseudodifferential Equations on a Half-line


  • Nakao Hayashi, Osaka University, Japan
  • Elena Kaikina, Technological Institute of Morelia, Mexico.

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.
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Mathematicians, Physicists, Engineers and graduate students.


Book information

  • Published: January 2004
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-51569-8


"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.

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