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math.AP2025
Mass threshold for global existence in chemotaxis systems with critical flux limitation
Xuan Mao, Hengling Wang, Jianlu Yan
This paper investigates the flux-limited chemotaxis system, proposed by Kohatsu and Senba~(2025), \begin{equation*} \begin{cases} u_t = Δu -\nabla\cdot(u|\nabla v|^{α-2}\nabla v),\…
math.AP2020
When do Keller-Segel systems with heterogeneous logistic sources admit generalized solutions?
Jianlu Yan, Mario Fuest
We construct global generalized solutions to the chemotaxis system \begin{align*} \begin{cases} u_t = Δu - \nabla \cdot (u \nabla v) + λ(x) u - μ(x) u^κ,\\ v_t = Δv - v + u \end{ca…
math.AP2018
Global generalized solutions to a nonlinear Keller-Segel equation with singular sensitivity
Jianlu Yan, Yuxiang Li
We consider the chemotaxis system \begin{eqnarray*} \begin{cases} \begin{array}{lll} \medskip u_t =Δu^m - \nabla(\frac{u}{v}\nabla v),&{} x\inΩ,\ t>0, \medskip v_t =Δv -uv,&{}x\inΩ…