On the fragmentation phenomenon in the population optimization problem

Abstract

In this paper, we study the population optimization problem in the logistic reaction-diffusion model. The issue of maximizing the total population in a heterogeneous environment has attracted the attention of many researchers. For the n n -dimensional box domain, it has recently been shown that resource fragmentation is better than concentration in order to maximize the total population when the diffusion rate is sufficiently small. As resource concentration is known to be beneficial for the survival of the species, this contrasting phenomenon is quite surprising. We proved that the fragmentation phenomenon occurs for any general bounded domains in R n \mathbb {R}^n if the diffusion rate is sufficiently small.