Structure of solutions to the differential equations arising in natural phenomina

自然现象中出现的微分方程解的结构

• 批准号: 09640191
• 负责人: YOSHIDA Kiyoshi
• 金额: $ 1.54万
• 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: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640191/
• 关键词: Keller-Segel system; Self-similar solution; global solutions; locations of blow up points; elliptic equations; two parameter problems; hyperbolic equations; Sobolev functions; 爆発点; Keller-Segel方程式; 関数空関

K.Yoshida, T.Senba and T.Nagi 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. K.Yoshida with Y.Mizutani and N.Muramoto studied the self-similar radial solution to the Keller-Segel system, and obtained the solutions of two types, one of which is in a low critical lebel, the other is in a high cirtical lebel, when a parameter is small. When the parameter is large, there is no self-similar radial solution. These results are extended to the non-radial case, which are prepared. T.Nagai and T.Senba considered the location of blow-up points, whose results are joint work with T.Suzuki and are announced at the conferances at R.M.I of Kyoto University ('97/6/23-6/25) and Kyushu University ('99/2/3-2/5). T.Shibata treated the eigenvalue problem to the nonlinear elliptic equations with two parameters and obtained the asymptotic properties of the variational eigenvalues. Y.Mizuta completed the results by Koskela concerning the uniqueness property for Sobolev functions. R.Ikehata derived an optimal decay rate of energy to initial-boundary problem of hyperbolic equations under geometric conditions on the bounbary.

K.Yoshida、T.Senba和T.Nagi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。K.Yoshida，Y.Mizutani和N.Muramoto研究了Keller-Segel系统的自相似径向解，得到了两种类型的解，当参数较小时，一种是在低临界区，另一种是在高临界区。当参数较大时，不存在自相似径向解。这些结果被推广到非径向的情况下，这是准备。T.永井和T.仙波考虑了爆破点的位置，其结果是与T.铃木的共同工作，并在京都大学R. M. I（'97/6/23-6/25）和九州大学（' 99/2/3-2/5）的会议上公布。T.柴田研究了双参数非线性椭圆型方程的特征值问题，得到了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。R.Ikehata在边界上的几何条件下，导出了双曲型方程初边值问题的最优能量衰减率。

项目成果

Y.Mizutani,N.Muramoto,K.Yoshida: "Self-similar radial soluitons to a parabolic system modelling chemotaxis via vari-ational method" Hiroshima Math.J.29. 145-160 (1999)

Y.Mizutani，N.Muramoto，K.Yoshida：“通过变分方法模拟趋化性的抛物线系统的自相似径向解”Hiroshima Math.J.29。

T.Nagai, T.Senba and K.Yoshida: "Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis" Func.Ekvacioj. 40. 411-433 (1997)

T.Nagai、T.Senba 和 K.Yoshida：“Trudinger-Moser 不等式在趋化抛物线系统中的应用”Func.Ekvacioj。

T.Shibata: "Asymptotic profiles of Variational Eigen-values of Two-Parameter Non-linear Strum-Liouville Problems" Math.Mech.Appl.Sci.21. 1619-1635 (1998)

T.Shibata：“二参数非线性 Strum-Liouville 问题的变分特征值的渐近轮廓”Math.Mech.Appl.Sci.21。

J.I.Diaz, T.Nagai and J.-M. Rakotoson: "Symmetrization techniques on unbounded domains : Application to a chemotaxis system on R^N" J.Differential Equations. (in press).

J.I.迪亚兹、T.Nagai 和 J.-M.

R.Ikehata, T.Matsuyama and M.Nakao: "Global solutions to the initial-boundary value problem for the quasilinear visco-elastic wave equation with a perturbtion." Funk.Ekvac.40-2. 293-312 (1997)

R.Ikehata、T.Matsuyama 和 M.Nakao：“具有摄动的拟线性粘弹性波动方程的初始边值问题的全局解。”