A class of invasion models in ecology with a free boundary and with cross-diffusion and self-diffusion

Abstract

In this paper we investigate a class of two-species invasion models with a free boundary and with cross-diffusion and self-diffusion in interval [0,+∞), where the native species occupies the whole environment [0,+∞), and the invasion species invade into the habitat of the native species. The systems under consideration are strongly coupled, and the position of the free boundary is determined by the Stefan condition. The aim of this paper is to show the existence of a global classical solution for the free boundary problems by using suitable transformations, the contraction mapping theorem and various estimates. Applications are given to the classical competition and predator-prey models with cross-diffusion and self-diffusion.