| Project/Area Number |
26610027
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
Takagi Izumi 東北大学, 理学研究科, 名誉教授 (40154744)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMAMOTO Hiroko 明治大学, 研究・知財戦略機構, 研究推進員 (10759153)
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| Research Collaborator |
LI Ying Harbin Institute of Technology
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 反応拡散方程式 / パターン形成 / 多成分 / 非拡散性成分 / 拡散性成分 / 不連続定常解 / 退化型反応拡散系 / 第一種不連続性をもつ定常解 / 安定性 / 拡散成分と非拡散成分 / 反応拡散系 / 不連続定常解の安定性 / 分岐解 / 非拡散性種 / 受容体―結合基反応 / 非拡散性物質 |
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| Outline of Final Research Achievements |
A standard approach to modeling biological pattern formation has been based on the idea that the interaction between a slowly diffusing activator and a rapidly diffusing inhibitor results in spontaneous formation of spatial patterns. However, if the activator is a receptor attached on the cell membrane, it does not diffuse. Lately, reaction-diffusion models with non-diffusive activator and diffusive inhibitor have been proposed. In this project we studied rigorously the existence and stability of steady-state solutions of such model systems. We proved that there exist two types of steady states. Type I: the activator has jump discontinuity (but the inhibitor is continuous), and Type II: the activator is continuous. In addition, there exist continua of discontinuous steady states. Moreover, discontinuous steady states are stable, while continuous steady states are stable.
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