Zeitschrift für angewandte Mathematik und Physik

, Volume 66, Issue 5, pp 2143–2160 | Cite as

The selection for dispersal: a diffusive competition model with a free boundary

  • Jie WangEmail author


This paper considers the population dynamics of an invasive species and a resident species, using a diffusive competition model in a radially symmetric heterogeneous environment with a free boundary. We assume that the resident species diffuses and expands in \({\mathbb{R}^n}\) , and the invasive species initially resides in a finite ball, but invades the environment with a spreading front that evolves as the free boundary. Our investigation aims to understand how the model dynamics are affected by the dispersal rate \({d_u}\) , expansion capacity \({\mu}\) and initial number u 0 of the invasive species. We show that a spreading–vanishing dichotomy exists and obtain the sharp criteria for spreading and vanishing by varying the parameters d u , \({\mu}\) and u 0. For the invasive species, we found an unconditional selection for slow dispersal rate, but a conditional selection for fast dispersal rate, that is, the selection for fast dispersal depends on the expansion capacity and initial number of the invasive species.


Diffusive competition model Invasive population Selection for dispersal Free boundary Spreading–vanishing dichotomy 

Mathematics Subject Classification

35K20 35R35 35J60 92B05 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China

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