4 papers · 1 filter
Sharp threshold for a one-dimensional thin film equation in the supercritical case
Shen Bian
We study a one-dimensional thin film equation combining competitive effects of aggregation and repulsion, where repulsion is modeled by fourth-order diffusion and aggregation by ba…
Steady states and dynamics of a higher dimensional thin film equation
Shen Bian
We study a higher-dimensional thin film equation that incorporates competitive effects between aggregation and repulsion, where repulsion is modeled by fourth-order diffusion and a…
Critical threshold for a two-species chemotaxis system with the energy critical exponent
Shen Bian
We consider a two-species chemotaxis model in featuring nonlinear porous medium-type diffusion and nonlocal attractive power-law interaction. Here, the nonlinear di…
The Keller-Segel model with mass critical exponent
Shen Bian, Yichen Zou
We consider a Keller-Segel model with non-linear porous medium type diffusion and non-local attractive power law interaction, focusing on potentials that are less singular than New…