Please use this identifier to cite or link to this item:
https://hdl.handle.net/1959.11/7482
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 | Handle Link: | https://hdl.handle.net/1959.11/7482 | 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: | United States of America | ISSN: | 1095-7154 0036-1410 |
Fields of Research (FoR) 2008: | 010110 Partial Differential Equations | Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences | Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal |
---|---|
Appears in Collections: | Journal Article |
Files in This Item:
File | Description | Size | Format |
---|
SCOPUSTM
Citations
368
checked on Jan 13, 2024
Page view(s)
1,166
checked on Feb 4, 2024
Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.