2010 Fiscal Year Final Research Report
Gevrey theory for singular first-order partial differential equations in complex domains
| Project/Area Number |
19740078
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Okayama University of Science |
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Principal Investigator |
HIBINO Masaki Okayama University of Science, 工学部, 准教授 (10441461)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 関数方程式論 / 複素解析 / 発散級数 / 総和可能性 / 解析接続 / 関数空間論 / 縮小写像 |
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| Research Abstract |
We studied first-order partial differential equations with singular points. Firstly, we gave conditions which ensure the existence and the uniqueness of formal power series solutions centered at the singular point, in forms of those for eigenvalues of some matrix determined by equations. Moreover, we gave conditions which assure the convergence of the formal solution. Secondly, we considered the linear equations called of nilpotent type, whose formal solution diverges, and we gave conditions under which the divergent solution is summable, in forms of global conditions (analytic continuation property, growth conditions or decreasing conditions) for coefficients of equations.
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Research Products
(7 results)
