Free boundary problems for the diffusive competition system in higher dimension with sign-changing coefficients

TL;DR

This paper studies free boundary problems for a higher-dimensional Lotka-Volterra competition system with sign-changing coefficients, analyzing species invasion dynamics and long-term behavior under radial symmetry.

Contribution

It introduces new free boundary models for multi-dimensional competition with sign-changing coefficients and characterizes conditions for species spreading and persistence.

Findings

Derived conditions for successful species invasion.

Established criteria for invasion failure.

Analyzed long-term behavior of species under spreading conditions.

Abstract

In this article we investigate two free boundary problems for a Lotka-Volterra competition system in a higher space dimension with sign-changing coefficients. One may be viewed as describing how two competing species invade if they occupy an initial region, the other describes the dynamical process of a new competitor invading into the habitat of a native species. For simplicity, it is assumed that the environment is radially symmetric. The main purpose of this article is to understand the asymptotic behavior of competing species spreading via a free boundary. We derive some sufficient conditions for species spreading success and spreading failure. Moreover, when spreading successfully, we provide the long time behavior of solutions.