Spreading dynamics for the Lotka-Volterra system with general initial supports: the strong competition

This paper studies the spreading dynamics of a high-dimensional strong competition Lotka-Volterra system where two species initially occupy disjoint measurable (possibly unbounded) subsets in ${\mathbb{R}}^N$, which are called initial support. Recently, Hamel and Rossi [14] introduced some new geometric notions, such as bounded or unbounded directions and positive-distance interior, for single-species equations with general initial supports. Under these notions and appropriate assumptions, we characterize directional spreading behavior for the two-species system: precise spreading speeds and sets for both species are derived.