偏微分方程讨论班
ECNU PDE Seminar
报告题目: Kinetics Causing the Collapse of Patterns
演讲人: Prof. Izumi Takagi
Tohoku University
时间: 2010年6月21日(星期一)下午1:30--2:30
地点: 华东师大闵行校区数学系102报告厅
Abstract.
Gierer and Meinhardt proposed a reaction-diffusion system comprised of an activator and an inhibitor to model transplantation experiments on hydra. If the equations do not contain terms independent of the activator and the inhibitor, then it is numerically observed that some solutions of the initial-boundary value problem starting from almost constant initial data develop spatial inhomogeneity at first, then begin to oscillate, and eventually converge uniformly to zero.
Since the equation has a term with the inhibitor in the denominator, this limit is not a stationary solution. This phenomenon, called the collapse of patterns, seems to be known among people doing computer simulations, but has never been reported in literature.
In this talk we prove rigorously that under certain conditions patterns do collapse, and study what happens if we perturb the system slightly to understand the mechanism that causes the collapse of patterns.