2016 Fiscal Year Final Research Report
Mathematical and numerical modeling for migration of Plecoglossus altivelis considering uncertainties
| Project/Area Number |
15H06417
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Rural environmental engineering/Planning
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| Research Institution | Shimane University |
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Principal Investigator |
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| Project Period (FY) |
2015-08-28 – 2017-03-31
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| Keywords | アユ / 回遊 / 最適制御理論 / ハミルトン・ヤコビ・ベルマン方程式 / 粘性解 / 斐伊川 |
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| Outline of Final Research Achievements |
We developed a new mathematical model for describing fish migration along 1-D rivers or connected graphs based on the optimal control theory. We showed that the derivation of the migration strategy reduces to finding a solution to a Hamilton-Jacobi-Bellman equation: a nonlinear degenerate parabolic partial differential equation. We also showed that the equation admits a viscosity solution and discussed its practical implications. Accurate numerical schemes for stable computation of the HJB equation has also been developed in the project. In addition, macroscopic mathematical models for population dynamics of Plecoglossus altivelis (Ayu) in river environment was established and applied to finding cost-effective management of the fish population.
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| Free Research Field |
環境水理学，数理生物学
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