2020 Fiscal Year Research-status 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 Institution | Kyushu University |
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Principal Investigator |
タ・ビィエ トン 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 | Evolution equations / Strict solutions / Mild solutions / Wiener process / Forest kinematic model |
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| Outline of Annual Research Achievements |
A) We continued to study this evolution equation
dX+AXdt=[F_1(t)+F_2(X)]dt+G(t)dW(t).
The results include: 1) Existence of both mild solutions and strict solutions; 2) Regularities of these solutions. Roughly speaking, we showed that A^pX is (gamma) Holder continuous functions.
To obtain these results, we used the semigroup methods. The results now are published in Communications on Pure and Applied Analysis.
B) We constructed a forest kinematic model. We are going to apply the results in A) to study this model.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The coefficients in the forest model are very nonregular. The existence of solutions may be obtained but it is difficult to show the behavior of solutions.
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| Strategy for Future Research Activity |
A) We will prove the existence of solutions to the forest kinematic model that we have constructed. To do this, we will approximate the solutions by solutions of a more "regular" system. Then, we will study the behavior of solutions and make numerical simulations.
B) We will also consider a semilinear evolution equation with multiple noise:
dX+AXdt=[F_1(t)+F_2(X)]dt+G(t,X)dW(t).
The aim is to construct a solution to this kind of equations.
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| Causes of Carryover |
It was impossible to have face-to-face collaborations with international researchers due to coronavirus outbreak in this fiscal year. I would like to carry the amount to the next fiscal year. I do hope that the travel situation will be improved.
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Research Products
(1 results)
