Structure of solutions to Keller-Segel system

T.Nagi， Y.Naito和K.Yoshida研究了Keller-Segel系统，这是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。内藤和吉田与N.Muramoto一起研究了Keller-Segel系统的自相似解。然后将Keller-Segel系统简化为参数为σ的椭圆型方程，得到了两种类型的解，一种是低临界水平，另一种是高临界水平。当参数较大时，不存在自相似径向解。这意味着两个解决方案通过一个全局白化连接在一起。永井和玄叶忠和铃木忠一起考虑了爆炸点的位置。这些结果在每次会议或研讨会上公布，例如，1999年12月6日至10日在香港举行的IMS反应扩散系统研讨会，2000年7月19日至26日在卡塔尼亚举行的第三届世界非线性分析大会。H.Usami处理了二阶常微分方程的振动问题和变分特征值的渐近性质。Y.Mizuta补全了Koskela关于Sobolev函数唯一性的结果。

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.