The asymptotic analysis of an insect dispersal model on a growing domain

This paper is concerned about a reaction-diffusion equation on n-dimensional isotropically growing domain, which describes the insect dispersal. The model for growing domains is first derived, and the comparison principle is then presented. The asymptotic behavior of the solution to the reaction-diffusion problem is given by constructing upper and lower solutions. Our results show that the growth of 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 illustrate the analytical results.