1998 Fiscal Year Final Research Report Summary
The well-posedness of the Cauchy problems for degenerate parabolic eqations
| 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)
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| Project Period (FY) |
1997 – 1998
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| Keywords | wellposedness / degenerate / microlocal analysis / Hamitonian flow / smoothing effect / propagation of the singularities / removable singularities / ratio ergodic theorem |
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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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