增长区域上扩散的Logistic方程解的全局渐近性

Global Asymptotic Behavior of Solutions of Diffusive Logistic Type Equation on a Growing Domain

考虑了一个各向同性增长区域上扩散的Logistic型方程.首先给出了增长区域上的反应扩散模型;然后利用比较原理,通过构造合适的上下解得到了反应扩散问题解的渐近性态;最后给出了数值模拟,以验证理论结果的正确性.

In this paper,we consider a diffusive logistic type equation on an isotropically growing domain.The model for growing domains is first presented,and the comparison principle is then obtained.By the construction of upper and lower solutions,the asymptotic behavior of temporal solutions to the reaction-diffusion problem is given.Numerical simulations are performed to verify our theoretical results.