| Project/Area Number |
21540164
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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 | Tokyo Institute of Technology |
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Principal Investigator |
MURATA Minoru 東京工業大学, 大学院・理工学研究科, 教授 (50087079)
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| Co-Investigator(Kenkyū-buntansha) |
SHIGA Hiroshige 東京工業大学, 大学院・理工学研究科, 教授 (10154189)
UCHIYAMA Kouhei 東京工業大学, 大学院・理工学研究科, 教授 (00117566)
MIYAMOTO Yasuhito 東京工業大学, 大学院・理工学研究科, 助教 (90374743)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 解析学 / 関数方程式 / 関数解析学 / 確率論 / 放物型方程式 / 熱核 / 積分表示 / 楕円型方程式 / グリーン関数 / 半小摂動 / マルチン境界 / 非負値解 |
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| Research Abstract |
We investigated the structure of nonnegative solutions to parabolic equations in cylinders on Riemannian manifolds, and gave explicit integral representation formulas for any solutions under the general and optimal condition that the constant function 1 is a semismall perturbation of the associated elliptic operator ; whose geometric characterization was also given in the case of the heat equation on rotationally symmetric Riemannian manifolds. Furthermore, by using the characterization and giving a sharp sufficient condition for the uniqueness of nonnegative solutions to the Cauchy problem, we determined the structure of nonnegative solutions to the heat equation on rotationally symmetric Riemannian manifolds.
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