2013 Fiscal Year Final Research Report
Mathematical studies for nonlocal effect on emergence of localized patterns in dissipative systems and applications
| Project/Area Number |
22340022
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Ryukoku University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
JIMBO Shuichi 北海道大学, 大学院・理学研究科, 教授 (80201565)
OGAWA Toshiyuki 明治大学, 先端数理科学研究科, 教授 (80211811)
MIYAMOTO Yasuhito 東京大学, 大学院・数理科学研究科, 准教授 (90374743)
MACHIDAQ Masahiko 独立行政法人日本原子力研究開発機構, システム計算科学センター, 研究主幹 (60360434)
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| Co-Investigator(Renkei-kenkyūsha) |
ISHIHARA Shuji 東京大学, 大学院・総合文化研究科, 助教 (10401217)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 散逸系 / 局在パターン / 非局所効果 / 反応拡散系 / パターン形成 / 安定性解析 / 分岐解析 / 非線形偏微分方程式 |
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| Research Abstract |
There are various dissipative systems which are proposed as mathematical models describing pattern formations. In particular, corresponding solutions to pattern formations of reaction-diffusion systems have been much studied. In this research we have shown a new mathematical mechanism for nonlocal effects working in emergence of localized patterns. More specifically, we have studied 2-component reaction-diffusion systems with conservation of mass and proved that the nonlocal effect coming from the mass conservation is connected to the stability of the localized pattern. We also have developed the mathematical method and applied it to other model equations.
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