| 研究課題/領域番号 |
19K14555
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| 研究機関 | 九州大学 |
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研究代表者 |
タ・ビィエ トン 九州大学, 農学研究院, 准教授 (30771109)
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| 研究期間 (年度) |
2019-04-01 – 2023-03-31
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| キーワード | Evolution equations / Strict solutions / Mild solutions / Wiener process / Forest kinematic model |
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| 研究実績の概要 |
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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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
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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| 今後の研究の推進方策 |
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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| 次年度使用額が生じた理由 |
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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