2004 Fiscal Year Final Research Report Summary
Studies on the applications of the theory of viscosity solutions to some singular perturbation problems
| Project/Area Number |
14540117
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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 | Kobe University (2004)
神戸商船大学 (2002-2003) |
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Principal Investigator |
ISHII Katsuyuki Kobe University, Faculty of Maritime Sciences, Associate Professor, 海事科学部, 助教授 (40232227)
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| Co-Investigator(Kenkyū-buntansha) |
MARUO Kenji Kobe University, Faculty of Maritime Sciences, Professor, 海事科学部, 教授 (90028225)
KAGEYAMA Yasuo Kobe University, Faculty of Maritime Sciences, Lecturer, 海事科学部, 講師 (70304136)
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| Project Period (FY) |
2002 – 2004
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| Keywords | motion by mean curvatute / numerical algorithm / viscosity solutions / degenerate elliptic partial differential equations |
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| Research Abstract |
Katsuyuki Ishii studied a numerical algorithm for motion by mean curvature, which is proposed by Bence, Merriman and Osher and obtained the following results
1.I gave a proof of convergence showing how the mean curvature flow equation is derived from this algorithm. (This is a joint work with Yoko Goto and Takayoshi Ogawa.)
2.I obtained the rate of convergence of this algorithm in the case of smoth motion by mean curvature. I also showed the optimality in the case of a circle evolving by curvature.
Kenji Maruo studied semilinear degenerate elliptic partial differential equations in the plane. He obtained the following
3.Assuming that the coefficients of the equation are radially symmetric, he proved that, under some growth conditions at infinity, the continuous viscosity solutions are radially symmetric
Yasuo Kageyama obtained the rate of convergence and some properties of modified Bernstein polynomials
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