Variational approach to pulse solutions in reaction-diffusion systems with spatial heterogeneity
| Project/Area Number |
17K05355
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Asahikawa Medical College |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 反応拡散系 / 変分法 / 数値解析 / 分岐解析 / 応用数学 / 反応拡散方程式系 |
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| Outline of Final Research Achievements |
By combining geometric singular perturbation techniques and an action functional approach, we analyzed localized solutions in a singularly perturbed three-component FitzHugh-Nagumo model. First, we derived criterions for the existence and stability of pinned pulse solutions in spatially heterogeneous media of a jump type and a bump type. We explicitly computed the pinning distance of a localized solution to the defect. Next we extended our action functional approach to the problem of traveling pulse solutions, in which we derived explicit conditions for their existence to determine the pulse width and propagating speed. We also deduced a necessary condition for the existence of traveling 2-pulse solutions and discussed about a saddle-node and Hopf bifurcations. All the results obtained from theoretical analyses were numerically confirmed.
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| Academic Significance and Societal Importance of the Research Achievements |
米国応用数学会主催の国際会議のミニシンポジウムを、研究期間内に２回（令和元年度、令和3年度）海外共同研究者らと連携して企画し、座長を行った。平成３０年度には日豪連携研究集会を企画し、北海道で開催した。日本、オーストラリア、台湾の研究者を中心に、貴重な情報交換、研究交流の場となった。これらの国際研究集会で共同研究について成果発表し、内容を欧文論文にまとめて国際誌 Journal of Dynamics and Differential Equations, 及び SIAM Journal of Applied Dynamical Systems から公刊した。
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Report
(6 results)
Research Products
(33 results)
