Para-differential calculus and applications to the Cauchy problem for nonlinear systems /
Author / Creator: | Métivier, Guy. |
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Imprint: | [Pisa, Italy] : Edizioni della Normale, c2008. |
Description: | xi, 140 p. ; 24 cm. |
Language: | English |
Series: | CRM series ; 5 CRM series (Pisa, Italy) ; 5. |
Subject: | |
Format: | Print Book |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7629653 |
Summary: | 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 Schr#65533;dinger equations which arise in various models of wave propagation. |
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Item Description: | "These notes originate from a graduate course given at the University of Pisa during the spring semester 2007"--Pref. |
Physical Description: | xi, 140 p. ; 24 cm. |
Bibliography: | Includes bibliographical references (p. [137]-138). |
ISBN: | 9788876423291 887642329X 8876423291 |