抄録
We construct a dynamical system for a reaction–diffusion system due to Murray, which relies on the use of the Thomas system nonlinearities and describes the formation of animal coat patterns. First, we prove existence and uniqueness of global positive strong solutions to the system by using semigroup methods. Second, we show that the solutions are continuously dependent on initial values. Third, we show that the dynamical system enjoys exponential attractors whose fractal dimensions can be estimated. Finally, we give a numerical example.
| 元の言語 | 英語 |
|---|---|
| ページ（範囲） | 525-564 |
| ページ数 | 40 |
| ジャーナル | Journal of Elliptic and Parabolic Equations |
| 巻 | 4 |
| 発行部数 | 2 |
| DOI | |
| 出版物ステータス | 出版済み - 12 1 2018 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
- Numerical Analysis
これを引用
Dynamical system for animal coat pattern model. / Ta, Ton Viet.
：: Journal of Elliptic and Parabolic Equations, 巻 4, 番号 2, 01.12.2018, p. 525-564.研究成果: ジャーナルへの寄稿 › 記事
}
TY - JOUR
T1 - Dynamical system for animal coat pattern model
AU - Ta, Ton Viet
PY - 2018/12/1
Y1 - 2018/12/1
N2 - We construct a dynamical system for a reaction–diffusion system due to Murray, which relies on the use of the Thomas system nonlinearities and describes the formation of animal coat patterns. First, we prove existence and uniqueness of global positive strong solutions to the system by using semigroup methods. Second, we show that the solutions are continuously dependent on initial values. Third, we show that the dynamical system enjoys exponential attractors whose fractal dimensions can be estimated. Finally, we give a numerical example.
AB - We construct a dynamical system for a reaction–diffusion system due to Murray, which relies on the use of the Thomas system nonlinearities and describes the formation of animal coat patterns. First, we prove existence and uniqueness of global positive strong solutions to the system by using semigroup methods. Second, we show that the solutions are continuously dependent on initial values. Third, we show that the dynamical system enjoys exponential attractors whose fractal dimensions can be estimated. Finally, we give a numerical example.
UR - http://www.scopus.com/inward/record.url?scp=85070908180&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85070908180&partnerID=8YFLogxK
U2 - 10.1007/s41808-018-0028-z
DO - 10.1007/s41808-018-0028-z
M3 - Article
AN - SCOPUS:85070908180
VL - 4
SP - 525
EP - 564
JO - Journal of Elliptic and Parabolic Equations
JF - Journal of Elliptic and Parabolic Equations
SN - 2296-9020
IS - 2
ER -