The longtime behavior of the model with nonlocal diffusion and free boundaries in online social networks

Meng Zhao; Meng Zhao

doi:10.3934/era.2020063

Electronic Research Archive

2020, Volume 28, Issue 3: 1143-1160. doi: 10.3934/era.2020063

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The longtime behavior of the model with nonlocal diffusion and free boundaries in online social networks

Meng Zhao ^,

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China

Received: 01 May 2020 Revised: 01 May 2020
35K57, 45G15, 35R35, 35B40

In this paper we consider a free boundary problem with nonlocal diffusion describing information diffusion in online social networks. This model can be viewed as a nonlocal version of the free boundary problem studied by Ren et al. (Spreading-vanishing dichotomy in information diffusion in online social networks with intervention, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019) 1843–1865). We first show that this problem has a unique solution for all $ t>0 $, and then we show that its longtime behaviour is determined by a spreading-vanishing dichotomy. We also obtain sharp criteria for spreading and vanishing, and show that the spreading always happen if the diffusion rate of any one of the information is small, which is very different from the local diffusion model.
- Social networks,
- nonlocal diffusion,
- free boundary,
- spreading and vanishing
Citation: Meng Zhao. The longtime behavior of the model with nonlocal diffusion and free boundaries in online social networks[J]. Electronic Research Archive, 2020, 28(3): 1143-1160. doi: 10.3934/era.2020063

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Abstract

In this paper we consider a free boundary problem with nonlocal diffusion describing information diffusion in online social networks. This model can be viewed as a nonlocal version of the free boundary problem studied by Ren et al. (Spreading-vanishing dichotomy in information diffusion in online social networks with intervention, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019) 1843–1865). We first show that this problem has a unique solution for all $ t>0 $, and then we show that its longtime behaviour is determined by a spreading-vanishing dichotomy. We also obtain sharp criteria for spreading and vanishing, and show that the spreading always happen if the diffusion rate of any one of the information is small, which is very different from the local diffusion model.

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