Analysis of Reaction-Diffusion Systems and Related Nonlinear Problems

反应扩散系统及相关非线性问题的分析

• 批准号: 21540229
• 负责人: YAMADA Yoshio
• 金额: $ 2.83万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540229/
• 关键词: 非線形現象; 反応拡散方程式; 非線形拡散; 自由境界問題; 数理生態学; 正値定常解; 人口モデル; 侵入モデル; 大域解

This research project is concerned with the mathematical formulation of non-uniformity of species in mathematical ecology such as the segregation of two competing species and the spreading of invasive species. These phenomena are described by reaction-diffusion equations with population densities as unknown functions. We have obtained satisfactory results on the structure of positive steady-states for two-species models with nonlinear diffusion and the mechanism of spreading and vanishing for free boundary problems in invasion models.

该研究项目涉及数学生态学中物种不均匀性的数学表述，例如两个竞争物种的隔离和入侵物种的传播。这些现象通过反应扩散方程来描述，其中群体密度为未知函数。我们在非线性扩散的两物种模型的正稳态结构以及入侵模型中自由边界问题的扩散和消失机制方面取得了令人满意的结果。

项目成果

Lotka-Volterra competition systems with cross-diffusion and related problems

具有交叉扩散的Lotka-Volterra竞争系统及相关问题

• 发表时间: 2010
• 作者: Ogasawara;M.;Shintani;M.;Watanabe;S.;Sakamoto;T.;Nakajima;K.;Takahashi;T.;Shuya Kushida;Yoshio Yamada
• 通讯作者: Yoshio Yamada

Spreading and vanishing for free boundary problems arising in mathematical biology

数学生物学中出现的自由边界问题的传播和消失

• 发表时间: 2012
• 作者: Y. Muroya;Y. Enatsu and Y. Nakata;角大輝;井口達雄;高野恭一;塩路直樹;大山陽介;T.Kojima;M. Kuroda and Y. Muroya;井口達雄;Yoshio Yamada
• 通讯作者: Yoshio Yamada

Limiting behavior of positive steady-states for the Lotka-Volterra competition with large cross-diffusion

具有大交叉扩散的 Lotka-Volterra 竞争的正稳态的限制行为

• 发表时间: 2009
• 作者: E.Messina;Y.Muroya;E.Russo;A.Vecchio;Yoshio Yamada
• 通讯作者: Yoshio Yamada

Effect of cross-diffusion on the stationary problem for a preypredator model with a protection zone

交叉扩散对带保护区的捕食者模型的平稳问题的影响

• 发表时间: 2011
• 期刊: J. Differential Equations
• 作者: Yoshihiro Mizuta;Takao Ohno;Tetsu Shimomura and Naoki Shioji;Mike Hay;Tatsuo Iguchi;日合文雄;Shingo Takeuchi;Mikio Murata;H. Sumi;N.Shioji;T.Masuda;Kazuhiro Oeda
• 通讯作者: Kazuhiro Oeda

Stability and Hopf bifurcation of coexistence steady-states to an SKT model in spatially heterogeneous environment

• DOI: 10.3934/dcds.2009.24.489
• 发表时间: 2009-03
• 期刊: Discrete and Continuous Dynamical Systems
• 影响因子: 1.1
• 作者: Kousuke Kuto