Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary

Title
Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary
Publication Date
2010
Author(s)
Du, Yihong
( author )
OrcID: https://orcid.org/0000-0002-1235-0636
Email: ydu@une.edu.au
UNE Id une-id:ydu
Lin, Zhigui
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Society for Industrial and Applied Mathematics
Place of publication
United States of America
DOI
10.1137/090771089
UNE publication id
une:7650
Abstract
In this paper we investigate a diffusive logistic model with a free boundary in one space dimension. We aim to use the dynamics of such a problem to describe the spreading of a new or invasive species, with the free boundary representing the expanding front. We prove a spreading-vanishing dichotomy for this model, namely the species either successfully spreads to all the new environment and stabilizes at a positive equilibrium state, or it fails to establish and dies out in the long run. Sharp criteria for spreading and vanishing are given. Moreover, we show that when spreading occurs, for large time, the expanding front moves at a constant speed. This spreading speed is uniquely determined by an elliptic problem induced from the original model.
Link
Citation
SIAM Journal on Mathematical Analysis, 42(1), p. 377-405
ISSN
1095-7154
0036-1410
Start page
377
End page
405

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