| Project/Area Number |
09640198
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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 |
解析学
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| Research Institution | Ehime University |
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Principal Investigator |
SADAMATSU Takashi Ehime University, Faculty of Engineering, Professor, 医学部, 教授 (10025439)
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| Co-Investigator(Kenkyū-buntansha) |
INOUE Tomoki Ehime University, Faculty of Engineering, Lecturer, 工学部, 講師 (60253316)
IGARI Katsujyu Ehime University, Faculty of Engineering, Professor, 工学部, 教授 (90025487)
KAJITANI Kunihiko Tsukuba University, Dpartment of Mathematics, Professor, 数学系, 教授 (00026262)
KITAGAWA Keiichiro Ehime University, Faculty of Education, Professor, 教育学部, 教授 (00025404)
一ノ瀬 弥 愛媛大学, 工学部, 助教授 (80144690)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1997: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | wellposedness / degenerate / microlocal analysis / Hamitonian flow / smoothing effect / propagation of the singularities / removable singularities / ratio ergodic theorem / 漸近解 / 超局所解析 / 正則延長 / シンプレックティック変換 / ポジティブトレース |
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| Research Abstract |
We are concerned with the wellposedness of the Cauchy problem for partial differential equations. Sadamatsu, T.gave a necessary condition of the wellposedness for degenerate (in x) 1st order parabolic equations of the canonical form. The result will be appeared elsewhere. Kajitani, K.gave a sufficient condition of the wellposedness for degenerate (in t) parabolic equations, Schrodinger type equations and quasilinear hyperbolic equations. Further he treated the smoothing effect property for Schrodinger equation and he cleared the role of Hainitonian flow is important. IgariK.treated the Cauchy problem in the complex domain and gave a Property concerning the propagation of the singularities. lnoue, T.proved the ratio ergodic theorem in the case of one-dimentional transformation.
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