Different spreading speeds in a weak competition model with two free boundaries

Abstract

In this paper, we focus on the spreading behavior of a two-species weak competition system with two free boundaries in a spherically symmetric setting. This model may describe how two weakly competing species spread into the right empty space. When both two species spread successfully and one species cannot keep pace with the other one, it can be expected that two species spread asymptotically in a linear fashion but spread with different speeds. By the help of a semi-wave system and a construction of supersolution and subsolution, we establish the precise spreading speeds and population distribution of two weakly competing species, which provides a new spreading behavior. (C) 2019 Elsevier Inc. All rights reserved.