缩小区域上一类捕获模型解的渐近性

The asymptotic behavior of solution of a class harvesting model on a shrinking domain

研究n维空间中一类捕获模型在各向同性缩小区域上解的渐近稳定性.首先在缩小区域上给出反应扩散方程,然后由比较原理得到问题的上、下解,最后利用上、下解的方法推导反应扩散方程解的渐近稳定性.所得结果表明,区域缩小对正的稳态解有积极作用,而对平凡解有消极影响,数值模拟也说明了这一点.

This paper is concerned about the asymptotic stability of the solution to a reaction-diffu- sion problem, which describes a harvesting model on n-dimensional isotropically shrinking domain. The reaction-diffusion equation for shrinking domains is first derived, then the comparison principle is presented. The asymptotic behavior of the solution to the reaction-diffusion problem is given by constructing upper and lower solutions. The results show that shrinking domain takes a positive effect on the asymptotic stability of positive steady state solution, while it takes a negative effect on the asymptotic stability of the trivial solution. Numerical simulations are also performed to illus- trate the conclusion.