Dynamics for a nonlocal competition system with a free boundary

ABSTRACT

In this paper, we investigate a nonlocal reaction–diffusion competition model with a free boundary and discuss the long time behavior of species. The main objective is to understand the effect of the nonlocal term in the form of an integral convolution on the dynamics of competing species. Specially, for the weak competition case, when spreading occurs, we provide some sufficient conditions to prove that two competing species stabilize at a positive constant equilibrium state. Furthermore, for the case of successful spreading, we estimate the asymptotic spreading speed of the free boundary.

KEYWORDS:

• Dynamics
• competition model
• free boundary
• integral convolution

AMS SUBJECT CLASSIFICATIONS:

• 35K51
• 35R35
• 92B05
• 35B40

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is partially supported by PRC grant NSFC [11771380], [11401515].