The free boundary problem describing information diffusion in online social networks

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• 作者：Chengxia Lei^a ; Zhigui Lin^a ; ^{zglin68@hotmail.com} ; Haiyan Wang^b ; ^{Haiyan.Wang@asu.edu}
• 关键词：35K20 ; 35R35 ; 35J60 ; 92B05
• 刊名：Journal of Differential Equations
• 出版年：2013
• 出版时间：1 February, 2013
• 年：2013
• 卷：254
• 期：3
• 页码：1326-1341
• 全文大小：247 K

文摘

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.