A Predator-Prey Model With Free Boundary Under Shifting Climate

This paper deals with a free boundary problem under shifting climate which is used to describe the predator-prey model.The model represents the development and change relationship between two species as prey and predator when the climate environment changes from unfavorable to favorable.First,The existence and uniqueness of a global classical solution are given by invoking the Schauder fixed point theorem.Secondly,we obtain the spreadingvanishing dichotomy of species,i.e.,if h<∞,the species will eventually disappear.When h∞=∞,the species will spread and eventually reach a stable species density.Finally,we take afor the parameter,σφ(x)and σψ(x)as the initial value,study the dependence of the solution of the problem(uσ,vσ,hσ)and σ.When σ∈(0,σ*),the solution(uσ,vσ,hσ)disappears.Whenσ∈[σ*,∞),spreading happens for(uσ,vσ,hσ),where σ*≤σ*.