Project/Area Number  04804008 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Doshisha University 
Principal Investigator 
KAWASAKI Kohkichi Doshisha University, Science and Engineering Research Institute, Professor, 理工学研究所, 教授 (10150799)

Project Fiscal Year 
1992 – 1993

Project Status 
Completed(Fiscal Year 1993)

Budget Amount *help 
¥1,600,000 (Direct Cost : ¥1,600,000)
Fiscal Year 1993 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1992 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  reactiondiffusion equation / nonlinear equation / traveling wave / spatial pattern / chemotaxis / 反応拡散方程式 / 非線形方程式 / 空間パターン / 走化性 / Traveling wave 
Research Abstract 
There are many chemotactic phenomena where livings gather by response to gradient of some chemical substances, for example, bacterial colonies and aggregations of slime molds. These phenomena can be described by nonlinear reactiondiffusion equations, that is, nonlinear partial deferential equations of population density u(x, t) and concentration of chemical substance c(x, t). This research aims to obtain the condition of existence of solutions and the speed of traveling waves which are expandign with periodical tailes. By the numerical simulations, we have obtained the parameter values in which some spatial patterns with periodical spots appear. Also we have obtained dependency on parameter values for speed and wavelength of traveling waves. The equations have essentially five parameters and the appearance of spatial spots depends on strength of chemotaxis and decomposition rate of chemotactic substance. The spatial patterns obtained by numerical simulations give good agreement with the patterns that had been obtained by the experiments of bacterial culture. The numerical calculations are performed by the alternatingdierction implicit method on large 2dimensional lattice points (800x800).
