Geodesic
The Cauchy problem for systems through the normal form of systems and theory of weighted determinant
Matsumoto, Waichiro1
1 Department of Applied Mathematics and Informatics, Faculty of Science and Technology, Ryukoku University, Seta, 520-2194 Ohtsu, JAPAN
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 18, 29 p.

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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 ∞ well-posedness (Levi condition).

Keywords: 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

Matsumoto, Waichiro 1

1 Department of Applied Mathematics and Informatics, Faculty of Science and Technology, Ryukoku University, Seta, 520-2194 Ohtsu, JAPAN 
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     title = {The {Cauchy} problem for systems through the normal form of systems and theory of weighted determinant},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
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     pages = {1--29},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {1998-1999},
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     mrnumber = {1721336},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEDP_1998-1999____A18_0/}
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Matsumoto, Waichiro. The Cauchy problem for systems through the normal form of systems and theory of weighted determinant. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 18, 29 p.. http://geodesic.mathdoc.fr/item/SEDP_1998-1999____A18_0/