A Free Boundary Problem For Three Information Diffusing In Online Social Networks

In this paper, we have investigated a partial model with a free boundary x=h(t), which describes three information diffusion in online social networks in a one-dimensional habi-tat.Firstly, in the second part of this paper, it gives that the free boundary problem (FBP) has unique positive solution (u, v, w, h), and makes further estimates for u(x, t),v(x, t),w(x, t) and h(t). And then a spreading-vanishing dichotomy is established by Theorem (3.1) and Theorem (3.2), which means that either the three information vanish eventually if the free boundary stays within a boundary, or the three information spread successfully if the free boundary can pass the threshold in part three. At last, it reveals that the three information will tend to the equilibrium if spreading happen on the condition m=n which suppose the information A and B have the same impact with information C in part four, and (5.1) shows that for large time, the free boundary moves at a asymptotic speed which cannot be faster than the minimal speed for the traveling wave solutions if spreading happens in the section five of this paper.