CRM Series

Para-Differential Calculus and Applications to the Cauchy Problem for Nonlinear Systems

Authors: Métivier, Guy

  • Presents a comprehensive exposition of the para-differential calculus for beginners
  • Provides a continuous exposition of the symmetrizer method from the constant coefficient equation to the variable coefficient case
  • Details the application to systems of Schrödinger equations
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About this Textbook

The main aim is to present at the level of beginners several modern tools of micro-local analysis which are useful for the mathematical study of nonlinear partial differential equations. The core of these notes is devoted to a presentation of the para-differential techniques, which combine a linearization procedure for nonlinear equations, and a symbolic calculus which mimics or extends the classical calculus of Fourier multipliers. These methods apply to many problems in nonlinear PDE’s such as elliptic equations, propagation of singularities, boundary value problems, shocks or boundary layers. However, in these introductory notes, we have chosen to illustrate the theory on two selected and relatively simple examples, which allow becoming familiar with the techniques. They concern the well posed-ness of the Cauchy problem for systems of nonlinear PDE's, firstly hyperbolic systems and secondly coupled systems of Schrödinger equations which arise in various models of wave propagation.

Buy this book

Softcover $34.95
price for USA
  • ISBN 978-88-7642-329-1
  • Free shipping for individuals worldwide
  • This title is currently reprinting. You can pre-order your copy now.

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Bibliographic Information

Bibliographic Information
Book Title
Para-Differential Calculus and Applications to the Cauchy Problem for Nonlinear Systems
Authors
Series Title
CRM Series
Series Volume
5
Copyright
2008
Publisher
Edizioni della Normale
Copyright Holder
Edizioni della Normale
Softcover ISBN
978-88-7642-329-1
Edition Number
1
Number of Pages
XI, 140
Topics