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

By Yihong Du, Zhigui Lin. 2013

194 citations recorded by the source corpus.

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 by the reaction terms), we show that a spreading-vanishing dichotomy holds, namely, as $t\to\infty$, either $h(t)\to\infty$ and $(u,v)\to (u^*,0)$, or $\lim_{t\to\infty} h(t)<\infty$ and $(u,v)\to (0,v^*)$, where $(u^*,0)$ and $(0, v^*)$ are the semitrivial steady-states of the system. Moreover, when spreading of $u$ happens, some rough estimates of the spreading speed are also given. When $u$ is an inferior competitor, we show that $(u,v)\to (0,v^*)$ as $t\to\infty$.

Subfields: Genetics, Mathematical Physics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/92e0baf9e38e6fafc77e18e8fa919f732d2394f9

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In Genetics

  1. Mingxin Wang
  2. Yang Zhang
  3. Meng Zhao
  4. Yihong Du
  5. Maolin Zhou
  6. Rui Peng
  7. Yonggang Zhao
  8. Chang-Hong Wu

In Mathematical Physics

  1. Mingxin Wang
  2. Yihong Du
  3. Yang Zhang
  4. Meng Zhao
  5. Maolin Zhou
  6. Rui Peng
  7. Zhigui Lin
  8. Junping Shi

In Public Health, Environmental and Occupational Health

  1. Mingxin Wang
  2. Yang Zhang
  3. Yihong Du
  4. Meng Zhao
  5. Maolin Zhou
  6. Rui Peng
  7. Junping Shi
  8. Peter Y. H. Pang

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