Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 254, Issue 3, Pages 1326-1341Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2012.10.021
Keywords
Diffusive logistic equation; Free boundary; Spreading; Vanishing; Social networks
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Funding
- NSFC of China [11071209, 11271197]
- NSF [CNS-1218212]
- Division Of Computer and Network Systems
- Direct For Computer & Info Scie & Enginr [1218212] Funding Source: National Science Foundation
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In this paper we consider a free boundary problem for a reaction-diffusion logistic equation with a time-dependent growth rate. Such a problem arises in the modeling of information diffusion in online social networks, with the free boundary representing the spreading front of news among users. We present several sharp thresholds for information diffusion that either lasts forever or suspends in finite time. In the former case, we give the asymptotic spreading speed which is determined by a corresponding elliptic equation. (C) 2012 Elsevier Inc. All rights reserved.
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