2022 Fiscal Year Final Research Report
Building a Theory of Regular Structures for Non-Autonomous and Quasi-Linear Rough Evolution Equations, and Applying the Theory to Forest Kinematic Ecosystems
| Project/Area Number |
19K14555
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Kyushu University |
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Principal Investigator |
Ta Viet Ton 九州大学, 農学研究院, 准教授 (30771109)
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | PDEs / SDEs / Evolution equation / swarming behavior / forest transition / evolution equations / strict solutions |
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| Outline of Final Research Achievements |
1) We have constructed new concept, named strict solutions, to a a class of semilinear evolution equations in the paper:Ta, T.V., Strict solutions to stochastic semilinear evolution equations in M-type 2 Banach spaces. Communications on Pure & Applied Analysis, 20 (2021), 1867-1891. 2) We have investigated swarming behaviors: a) observed animal swarms avoiding predator to have a rule; b) constructed a mathematical model of
SDEs for predator-avoidance swarms by using the rule; c) performed simulations in some cases.+) Hartono, A.D., Nguyen, L.T.H., Ta, T.V.*: A stochastic differential equation model for predator-avoidance fish schooling. 39 pages, (https://doi.org/10.48550/arXiv.2210.03989). +) Hartono, A.D., Nguyen, L.T.H., Ta, T.V.*: A geometrical structure for predator-avoidance fish school. Proceedings of the Forum "Math-for-Industry" 2022.
3) We have constructed a SDE model and its global solutions for a forest transition of forest land, agricultural land, and abandonment land sizes.
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| Free Research Field |
PDEs, SDEs, Applied mathematics
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| Academic Significance and Societal Importance of the Research Achievements |
New concept, named strict solutions, to a a class of semilinear evolution equations has been introduced. In addition, the mechanism of swarming behaviors and forest transition is also verified using SDEs approach.
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