The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor

In this paper we consider the diffusive competition model consisting of an invasive species with density $u$ and a native species with density $v$, in a radially symmetric setting with free boundary. We assume that $v$ undergoes diffusion and growth in $\R^N$, and $u$ exists initially in a ball $\{r0$ is a given constant and $u(t,h(t))=0$. Thus the population range of $u$ is the expanding ball $\{r

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