Para-differential Calculus and Applications to <br />the Cauchy Problem for Nonlinear Systems
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | METIVIER, Guy | |
| dc.date.accessioned | 2024-04-04T02:52:05Z | |
| dc.date.available | 2024-04-04T02:52:05Z | |
| dc.date.issued | 2008 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192028 | |
| dc.description.abstractEn | These notes originate from a graduate course given at the University of Pisa during the <br />spring semester 2007. They were completed while the author was visiting the <br />Centro di Ricerca Matematica Ennio De Giorgi<br />in february 2008. <br />The main objective is to present at the level of beginners an introduction <br />to several modern tools of micro-local analysis which are useful for the mathematical study <br />of nonlinear partial differential equations. The guideline is to show how one can use the para-differential <br />calculus to prove energy estimates using para-differential symmetrizers, or to decouple<br />and reduce systems to equations. In these notes, we have concentrated <br />the applications on the well posed-ness of the Cauchy problem for nonlinear PDE's. <br />These notes are divided in three parts. Part I is an introduction to <br />evolution equations. After the presentation of physical examples, we give the bases of the analysis of systems with constant coefficients. In Part II, we give an elementary and self-contained presentation of the para-differential <br />calculus which was introduced by Jean-Michel Bony \cite{Bony} in 1979. Part III is devoted to two applications. <br />First we study quasi-linear hyperbolic systems.<br />The second application concerns the local in time well posedness of the <br />Cauchy problem for systems of Schödinger equations, <br />coupled though quasilinear interactions. | |
| dc.language.iso | en | |
| dc.title.en | Para-differential Calculus and Applications to <br />the Cauchy Problem for Nonlinear Systems | |
| dc.subject.hal | Mathématiques [math] | |
| bordeaux.page | 143 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | cel-00287554 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//cel-00287554v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2008&rft.spage=143&rft.epage=143&rft.au=METIVIER,%20Guy& |
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