Numerical aspects for the axisymmetric solution of a simplied Keller-Segel system

• Main Authors: HSU,CHUNG-HAN, 許鍾瀚
• Other Authors: CHO, CHIEN-HONG
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/49399515628546777025

碩士 === 國立中正大學 === 數學系應用數學研究所 === 104 === We consider the finite difference solutions for the parabolic-elliptic Keller-Segel system, which describes the aggregation of slime molds driven by a chemical substance. It was proved that its solution blows up in finite time on some conditions and it conserves the mass and preserves nonnegativity. In this paper, we compute the blow-up solutions and blow-up times with Schemes which conserves mass and does not conserves mass by Cho's algorithm proposed in [2]. One of the condition for blow-up is indefinite, so we want to check its necessity. To this end, we apply an algorithm in [3], which can numerically detect blow-up while we don't know weather the solution blows up in finite time. Keywords:Keller-Segel, blow-up time, finite difference method, numerically detect.