2010 Fiscal Year Final Research Report
Study on systems of partial differential equations applying the abstract algebra
| Project/Area Number |
19540202
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Ryukoku University |
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Principal Investigator |
MATSUMOTO Waichiro Ryukoku University, 理工学部, 教授 (40093314)
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| Co-Investigator(Kenkyū-buntansha) |
YOTSUTANI Shoji 龍谷大学, 理工学部, 教授 (60128361)
ITO Toshikazu 龍谷大学, 経済学部, 教授 (60110178)
NINOMIYA Hirokazu 明治大学, 理工学部, 准教授 (90251610)
NISHITANI Tatsuo 大阪大学, 理学研究科, 教授 (80127117)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 南雲型のCauchy=Kowalevskayaの定理 / 擬Jordan標準形 / 系の行列式理論 / p-parabolic system / 強双曲系 / 超弱双曲系 |
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| Research Abstract |
(1) We have shown that, for the Cauchy=Kowalevskaya theorem on a system, it is necessary that the system is similar to Kowalevskian accepting poles on symbols. On the sufficiency, we have succeeded to prove it on some models, but we need refine on the normal form in order to treat the general case. (2) On the systems with coefficients depending only on the time variable, it is necessary and sufficient for the strong hyperbolicity that the system is uniformly diagonalizable as a hyperbolic Fuchsian. (3) The study under the new definition of the p-parabolic system is not satisfactory.
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