The Cauchy problem for systems through the normal form of systems and theory of weighted determinant

Waichiro Matsumoto[1]

  • [1] Department of Applied Mathematics and Informatics, Faculty of Science and Technology, Ryukoku University, Seta, 520-2194 Ohtsu, JAPAN

Séminaire Équations aux dérivées partielles (1998-1999)

  • Volume: 1998-1999, page 1-29

Abstract

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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).

How to cite

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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 1998-1999 (1998-1999): 1-29. <http://eudml.org/doc/10968>.

@article{Matsumoto1998-1999,
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).},
affiliation = {Department of Applied Mathematics and Informatics, Faculty of Science and Technology, Ryukoku University, Seta, 520-2194 Ohtsu, JAPAN},
author = {Matsumoto, Waichiro},
journal = {Séminaire Équations aux dérivées partielles},
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; Levi condition; analytic well-posedness; well-posedness; Cauchy-Kowalevskaya theorem},
language = {eng},
pages = {1-29},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {The Cauchy problem for systems through the normal form of systems and theory of weighted determinant},
url = {http://eudml.org/doc/10968},
volume = {1998-1999},
year = {1998-1999},
}

TY - JOUR
AU - Matsumoto, Waichiro
TI - The Cauchy problem for systems through the normal form of systems and theory of weighted determinant
JO - Séminaire Équations aux dérivées partielles
PY - 1998-1999
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1998-1999
SP - 1
EP - 29
AB - 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).
LA - eng
KW - 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; Levi condition; analytic well-posedness; well-posedness; Cauchy-Kowalevskaya theorem
UR - http://eudml.org/doc/10968
ER -

References

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