Spreading speeds for a two-species competition-diffusion system
Abstract
We study in this article the behaviour of a system of logistic competition-diffusion equations with certain initial conditions. It models the invasion of a favorable habitat by two types of cells, which are competing for nutrients and cannot coexist. We show that the global behaviour depends mostly on the spreading speeds of each species alone. If the two species are absent from the right half-line x > 0, and the slowest one dominates the fastest one on x < 0, then the latter will invade the right space at its Fisher-KPP speed, and will be replaced by or will invade the former, depending on the parameters, at a slower speed.
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