Numerical analysis of attractors determined from nonlinear diffusion systems

由非线性扩散系统确定的吸引子的数值分析

• 批准号: 14540204
• 负责人: YAGI Atsushi
• 金额: $ 2.3万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540204/
• 关键词: Dynamical system; Attractor; Nonlinear diffusion system; Stability; Reliability; Simulation; Chemotaxis-growth model; Pattern formation; 走行性・増殖モデル; 数値解析

In 2002, we are concerned mainly with constructing stable and reliable discretization scheme for nonlinear parabolic systems. We invited Prof. Favini (Bologna) and Prof. Park (Pusan) who are both the experts in the theory of Abstract Parabolic Evolution Equations. We also contacted with many Japanese researchers to discuss the various subjects concerning to our project. By those activities, we succeeded in constructing a discretization scheme which is globally stable and has a global reliability for exponential attractors determined from nonlinear diffusion systems.In 2003, we are concerned mainly with systematic numerical computations of nonlinear parabolic systems in Physics, Engineering and Biology. We invited Prof. Efendiev (Stuttgart) who is the expert in the theory of Infinite Dimensional Dynamical Systems, and contacted with Prof. Mimura (Hiroshima) who is the presenter of a well-known chemotaxis-growth model. By those activities, we found out that the chemotaixis-growth model admits various pattern solutions, like the network pattern as a pattern With gradual change, the target and perforated target patterns as short range patterns and the honeycomb pattern, the stripe pattern, the perforated pattern and the moving spots pattern as long range patterns. The chemotaxis-growth system has therefore a very remarkable structure of pattern formation.

2002年，我们主要致力于构造稳定可靠的非线性抛物型方程组的离散格式。我们邀请了法维尼教授(博洛尼亚)和朴教授(釜山)，他们都是抽象抛物型发展方程理论方面的专家。我们还联系了许多日本研究人员，讨论了与我们项目有关的各种主题。通过这些活动，我们成功地构造了由非线性扩散系统确定的指数吸引子的全局稳定和全局可靠的离散化格式。2003年，我们主要关注物理、工程和生物学中的非线性抛物系统的系统数值计算。我们邀请了无限维动力系统理论的专家Efendiev教授(斯图加特)，并与广岛的Mimura教授联系，他是一个著名的趋化生长模型的提出者。通过这些活动，我们发现趋化生长模型可以接受多种模式解，如网络模式为渐变模式，靶标和穿孔目标模式为短程模式，蜂窝模式、条纹模式、穿孔模式和运动斑点模式为长程模式。因此，趋化-生长系统具有非常显著的图案形成结构。

项目成果

E.Nakaguchi, A.Yagi: "Numerical analysis for semilinear evolution equations of parabolic type"J.Comp.Appli.Math.. 159. 91-99 (2003)

E.Nakaguchi、A.Yagi：“抛物型半线性演化方程的数值分析”J.Comp.Appli.Math.. 159. 91-99 (2003)

Y.Takei, K.Osaki, T.Tsujikawa, A.Yagi (Cho, Kim, Ha 編集): "Differential Equations and Applications, Vol.4"Nova Science, New York(出版予定).

Y.Takei、K.Osaki、T.Tsujikawa、A.Yagi（Cho、Kim、Ha 编辑）：“微分方程和应用，第 4 卷”Nova Science，纽约（待出版）。

Nakaguchi, Yagi: "Numerical analysis for semilinear evolution equations of parabolic type"J.ComAppli.Math.. 159. 91-99 (2003)

Nakaguchi, Yagi：“抛物型半线性演化方程的数值分析”J.ComAppli.Math.. 159. 91-99 (2003)

M.Aida, A.Yagi: "Global attractor for approximate system of chemotaxis and growth"Dynam.Conti.Discrete Impuls.System Ser.A. 10・1-3. 309-315 (2003)

M.Aida、A.Yagi：“趋化性和生长的近似系统的全局吸引子”Dynam.Conti.Discrete Impuls.System Ser.A. 309-315。

Osaki, Tsujikawa, Yagi, Mimura: "Exponential attractor for a chemotaxis-growth system of equations"Nonlinear Analysis. 55. 119-144 (2002)

Osaki、Tsujikawa、Yagi、Mimura：“趋化生长方程组的指数吸引子”非线性分析。