This paper is concerned with a diffusive Lotka-Volterra type competitionsystem with a free boundary in one space dimension. Such a system may be usedto describe the invasion of a new species into the habitat of a nativecompetitor. We show that the longtime dynamical behavior of the system isdetermined by a spreading-vanishing dichotomy, and provide sharp criteria forspreading and vanishing of the invasive species. Moreover, we determine theasymptotic spreading speed of the invasive species when its spreading issuccessful, which involves two systems of traveling wave type equations, and ishighly nontrivial to establish.
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