Abstract
This paper is concerned with the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one and the other is a native one or both are invasive species. Our results seem to be the first that provide a precise spreading speed and profile for such a strong competition system. Among other things, our analysis relies on the construction of new types of supersolution and subsolution, which are optimal in certain sense.
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