An asymptotic expansion of the fundamental solution to the heat equation and its applications
| Project/Area Number |
21540194
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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 | University of Hyogo |
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Principal Investigator |
IWASAKI Chisato 兵庫県立大学, 大学院・物質理学研究科, 教授 (30028261)
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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 |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 放物型偏微分方程式 / 基本解 / 擬微分作用素 / リー群 / 指数 / フォッカープランク方程 / 固有函数展開 / 放物型方程式 / 退化 / べき零リー群 / ゼータ関数 / 漸近展開 / 熱方程式 / 固有値 / スペクトル関数 / 冪零リー群 / 国際研究者交流 / ドイツ / 指数宗理 |
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| Research Abstract |
The following three facts are shown through the construction of the fundamental solution to degenerate parabolic equations by means of the method of calculus of pseudo-differential operators :(1) Local index theorem holds for the Dirac Operators.(2) One can construct the fundamental solution in the exact form, which can be applied to obtain the eigenfunction expansions of the Fokker Planck operator.(3) The spectral zeta function of the degenerate operator, which is defined naturally on Nilmanilds, has the only one singularity.
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Report
(4 results)
Research Products
(31 results)
