Structure of solutions to Keller-Segel system

Keller-Segel 系统解的结构

• 批准号: 11640203
• 负责人: YOSHIDA Kiyoshi
• 金额: $ 2.05万
• 依托单位: HIROSHIMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640203/
• 关键词: Keller-Segel system; Self-similar solution; global blanch; locations of blow up points; chemotactic collapse; elliptic equation; oscllation problem; Sobolev functions; 楕円型方程式; 爆発; 大域解; 固有値問題; 双曲型方程式

T.Nagi, Y.Naito and K.Yoshida studied the Keller-Segel system which is the mathematical model describing chemotactic aggregation of cellular slime molds which move toward high cocentrations of chemical substance. Naito and Yoshida with N.Muramoto studied the self-similar solution to the Keller-Segel system. Then the Keller-Segel system is reduced to an elliptic equation with an parameter σ, and obtained solutions of two types, one of which is in a low critical lebel, the other is in a high cirtical lebel. When the parameter is large, there is no self-similar radial solution. This means two solutions are connected by a global blanch. Nagai with T.Senba and T.Suzuki considered the location of blow-up points. These results are announced at each conference or workshop e.g, IMS Workshop on Reaction-Diffusion Systems at HongKong (December 6-10, 1999), The Third World Congress of Nonlinear Analysis at Catania (July 19-26, 2000). H.Usami treated the oscillation problem to the second order ordinary differential equations and the asymptotic properties of the variational eigenvalues. Y.Mizuta completed the results by Koskela concerning the uniqueness property for Sobolev functions.

T.Nagi，Y.Naito和K.Yoshida研究了描述细胞黏菌向高浓度化学物质移动的趋化聚集的数学模型Keller-Segel系统。内藤和吉田与N.Muramoto研究了Keller-Segel系统的自相似解。然后将Keller-Segel系统化为一个含参数σ的椭圆型方程，得到了两类解，一类是在低临界边界，另一类是在高临界边界.当参数较大时，不存在自相似径向解。这意味着两个解通过全局漂白连接。永井与千场和铃木考虑了爆破点的位置。这些结果在每次会议或研讨会上公布，例如，在香港举行的IMS反应扩散系统研讨会（1999年12月6日至10日），在卡塔尼亚举行的第三届世界非线性分析大会（2000年7月19日至26日）。H.Usami将振动问题转化为二阶常微分方程及其变分特征值的渐近性质。Y.Mizuta完成了Kobola关于Sobolev函数的唯一性的结果。

项目成果

Y.Naito and H.Usami: "Oscillation criteria for quasilinear elliptic equations"Nonlinear Analysis. (発表予定).

Y.Naito 和 H.Usami：“拟线性椭圆方程的振荡准则”非线性分析（待提交）。

K.Kamo and H.Usami: "Asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations"Adv.Math.Sci.Appl.. 10. 673-688 (2000)

K.Kamo 和 H.Usami：“二阶拟线性常微分方程正解的渐近形式”Adv.Math.Sci.Appl.. 10. 673-688 (2000)

Y.Mizuta and T.Shimomura: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. 24・2. 457-465 (2000)

Y.Mizuta 和 T.Shimomura：“单位球中单调 BLD 函数的球面平均值的增长特性”Acad.Sci.Fenn.Ser.A.I.Math.. 24・2 (2000)。

N.Muramoto,Y.Naito and K.Yoshida: "Existance of self-similar solutions to a parabolic system modelling chemotaxis"Japan J.Indust.Appl.Math.. (発表予定).

N.Muramoto、Y.Naito 和 K.Yoshida：“抛物线系统建模趋化性的自相似解的存在”Japan J.Indust.Appl.Math..（待提交）。

Nagai: "Behavior of solutions to a parabolic-elliptic system modelling chemotaxis"J.Korean Math.Soc.. 37. 721-733 (2000)

Nagai：“模拟趋化性的抛物线-椭圆系统的解的行为”J.Korean Math.Soc.. 37. 721-733 (2000)