Longtime behavior of a free boundary model with nonlocal diffusion in online social networks

Phuong Le ()
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Phuong Le: University of Economics and Law

Partial Differential Equations and Applications, 2025, vol. 6, issue 3, 1-26

Abstract: Abstract This paper is concerned with a free boundary problem for a reaction–diffusion logistic equation with a nonlocal operator and a time-dependent growth rate. This problem arises as a model of information diffusion in online social networks, with the free boundaries representing the spreading front of news among users. We prove the existence of a sharp threshold for information diffusion that either lasts forever or suspends in finite time. In the former case, we show that the asymptotic spreading speed is either constant or accelerated in time depending on the nonlocal kernel. This feature makes the model more realistic than related models involving local operators in the literature.

Keywords: Reaction–diffusion equations; Free boundary problems; Nonlocal diffusion; Spreading speed; Social networks; 35K57; 35R35; 35K20; 91D30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00324-3

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