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Séminaire Équations aux dérivées partielles (Polytechnique)

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Waichiro Matsumoto
The Cauchy problem for systems through the normal form of systems and theory of weighted determinant
Séminaire Équations aux dérivées partielles (Polytechnique) (1998-1999), Exp. No. 18, 29 p.
Article PDF | Analyses MR 1721336 | Zbl 1059.35500
Mots clés: normal form of systems, p-determinant of matrix of pseudo-differential operators, p-evolution, the Cauchy-Kowalevskaya theorem for systems, $C^\infty $ well-posedness for systems

Résumé - Abstract

The author propose what is the principal part of linear systems of partial differential equations in the Cauchy problem through the normal form of systems in the meromorphic formal symbol class and the theory of weighted determinant. As applications, he choose the necessary and sufficient conditions for the analytic well-posedness ( Cauchy-Kowalevskaya theorem ) and $C^\infty $ well-posedness (Levi condition).

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