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Title: Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary
Contributor(s): Du, Yihong  (author); Lin, Zhigui (author)
Publication Date: 2010
DOI: 10.1137/090771089
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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.
Publication Type: Journal Article
Source of Publication: SIAM Journal on Mathematical Analysis, 42(1), p. 377-405
Publisher: Society for Industrial and Applied Mathematics
Place of Publication: Philadelphia, United States of America
ISSN: 0036-1410
Field of Research (FOR): 010110 Partial Differential Equations
Socio-Economic Outcome Codes: 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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