open access

https://doi.org/10.14943/doctoral.k14290

https://hdl.handle.net/2115/87170

ある粒子反応拡散系モデルの数学的取り扱いについて

英語

2020-12-25

Hokkaido University

57p

In the nature, we can state that the collective motion is one of the universal phenomena. Here, collective motion is the complex phenomena as the aggregation of several individuals which moves following ones rule, and is not described as simply sum of each individuals. We can see some example of such a collective motion in flog of birds, school of fishes, and bacteria, etc. For the purpose of understanding the basic mechanism of such collective motion, many experiments of self-driven materials, which are inanimate systems that do not depend on characteristics peculiar to living things, have been reported. At the same time, many theoretical analyzes using mathematical models are performed. In this paper, we state the result for a model equation derived from the motion of camphor disk. The first result shows the existence of unique solution to initial value problem for the model equation. In preceding studies, some mathematical results are obtained for the model equation,and the existence of the solutions to initial value problem are referred. But the proof does not exist. The second result states the existence of the solutions corresponds to non-trivial motion of two camphor disks. Our result reveals the conditions for existence and non-existence for the solution.

2020-12-25

甲第14290号

博士(理学)

(主査) 教授 長山 雅晴, 教授 栄 伸一郎, 教授 久保 英夫

理学院（数学専攻）

博士論文

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