Please use this identifier to cite or link to this item:
Title: Spreading and vanishing in nonlinear diffusion problems with free boundaries
Contributor(s): Du, Yihong  (author); Lou, Bendong (author)
Publication Date: 2015
Open Access: Yes
DOI: 10.4171/JEMS/568Open Access Link
Handle Link:
Open Access Link: Access Link
Abstract: We study nonlinear diffusion problems of the form ut = uxx + f (u) with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special f (u) of the Fisher-KPP type, the problem was investigated by Du and Lin [DL]. Here we consider much more general nonlinear terms. For any f (u) which is Ϲ¹ and satisfies f (0) = 0, we show that the omega limit set ω(u) of every bounded positive solution is determined by a stationary solution. For monostable, bistable and combustion types of nonlinearities, we obtain a rather complete description of the long-time dynamical behavior of the problem; moreover, by introducing a parameter σ in the initial data, we reveal a threshold value σ* such that spreading (limt→∞u = 1) happens when σ > σ*, vanishing (limt→∞u = 0) happens when σ < σ*, and at the threshold value σ*, ω(u) is different for the three different types of nonlinearities. When spreading happens, we make use of "semi-waves" to determine the asymptotic spreading speed of the front.
Publication Type: Journal Article
Grant Details: ARC/DP120100727
Source of Publication: Journal of the European Mathematical Society, 17(10), p. 2673-2724
Publisher: European Mathematical Society Publishing House
Place of Publication: Zurich, Switzerland
ISSN: 1435-9855
Field of Research (FOR): 010110 Partial Differential Equations
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Statistics to Oct 2018: Visitors: 71
Views: 71
Downloads: 0
Appears in Collections:Journal Article
School of Science and Technology

Files in This Item:
2 files
File Description SizeFormat 
Show full item record


checked on Nov 26, 2018

Page view(s)

checked on Mar 3, 2019
Google Media

Google ScholarTM



Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.