Spreading speed revisited: Analysis of a free boundary
model

Gary Bunting; Yihong Du; Krzysztof Krakowski; Gary Bunting; Yihong Du; Krzysztof Krakowski

doi:10.3934/nhm.2012.7.583

Networks and Heterogeneous Media

2012, Volume 7, Issue 4: 583-603. doi: 10.3934/nhm.2012.7.583

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Spreading speed revisited: Analysis of a free boundary model

1.
School of Science and Technology, University of New England, Armidale, NSW 2351

Received: 01 January 2012 Revised: 01 July 2012
35K20, 35R35, 35J60, 92B05.

We investigate, from a more ecological point of view, a free boundary model considered in [11] and [8] that describes the spreading of a new or invasive species, with the free boundary representing the spreading front. We derive the free boundary condition by considering a "population loss" at the spreading front, and correct some mistakes regarding the range of spreading speed in [11]. Then we use numerical simulation to gain further insights to the model, which may help to determine its usefulness in concrete ecological situations.
- Diffusive logistic equation,
- free boundary,
- spreading-vanishing dichotomy,
- invasive population,
- spreading speed
Citation: Gary Bunting, Yihong Du, Krzysztof Krakowski. Spreading speed revisited: Analysis of a free boundarymodel[J]. Networks and Heterogeneous Media, 2012, 7(4): 583-603. doi: 10.3934/nhm.2012.7.583

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Abstract

We investigate, from a more ecological point of view, a free boundary model considered in [11] and [8] that describes the spreading of a new or invasive species, with the free boundary representing the spreading front. We derive the free boundary condition by considering a "population loss" at the spreading front, and correct some mistakes regarding the range of spreading speed in [11]. Then we use numerical simulation to gain further insights to the model, which may help to determine its usefulness in concrete ecological situations.

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