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

@article{Du2013TheDC,
title={The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor},
author={Y. Du and Zhigui Lin},
journal={arXiv: Analysis of PDEs},
year={2013}
}

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 $\{r 0$ is a given constant and $u(t,h(t))=0$. Thus the population range of $u$ is the expanding ball $\{r<h(t)\}$, while that for $v$ is $\R^N$. In the case that $u$ is a superior competitor (determined… Expand