2011 Fiscal Year Final Research Report
Enclosures of solution curve of differential equations by computer-assisted proof
| Project/Area Number |
21540134
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
NAGATOU Kaori 九州大学, マス・フォア・インダストリ研究所, 准教授 (40326426)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 計算機援用証明 / 精度保証付き数値計算 / 非線形偏微分方程式 |
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| Research Abstract |
We developed a computer-assisted theory to verify the existence of the solutions for nonlinear elliptic boundary value problems with local uniqueness. We also proposed verified computations of eigenvalue exclosures for the linearization problems. Finally combining with developed method and the implicit function theorem, we introduced a procedure to enclose solution curves of nonlinear partial differential equations by computer-assisted proof and confirmed its effectiveness by some verified results.
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