2004 Fiscal Year Final Research Report Summary
Research of structure of stable spike solutions of Gierer-Meinhardt system in non-oonvex domain in two space dimensions
| Project/Area Number |
15540122
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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 | HIROSHIMA UNIVERSITY |
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Principal Investigator |
OHNISHI Isamu Hiroshima University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (30262372)
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| Co-Investigator(Kenkyū-buntansha) |
UEYAMA Daishin Hiroshima University, Graduate School of Science, Assistant, 大学院・理学研究科, 助手 (20304389)
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| Project Period (FY) |
2003 – 2004
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| Keywords | Gierer-Meinhardt / Liesegang phenomena / Colloid growth and dissolution / the exponential laws / reaction-diffusion system / pattern formation |
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| Research Abstract |
We have studied about structure of stable spike solutions of Gierer-Meinhardt system from the view point of pattern formation problem in reaction-diffusion system. We have been especially interested in pattern formation of Liesegang phenomena, which was discovered in 1896 by Professor Liesegang in Germany. We first made simulations of Keller-Rubinow model to verify that time law and spacing law hold and we made a mathematically rigorous proof of them by use of the model equation. Next, we noticed that Keller-Rubinow model cannot realize width of precipitation. Therefore, we improved the model equation by use of the theory of colloid growth and dissolution progressed by Professor S.Kai in Kyushu University. This is a very good model because it realizes the real chemical experiment. Especially, it realize the splitting and destroying phenomena of the ring pattern. Finally, we make a conjecture that the system has an essential instability and it causes the splitting and destroying phenomena of the ring pattern, and moreover the final pattern should be the checker board like pattern. This is a very interested result, so we talk about it in some international conferences and symposiums to report it in references in the below 11..
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Research Products
(10 results)
