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math.AP2016★ 122 cited
How strong a logistic damping can prevent blow-up for the minimal Keller-Segel chemotaxis system?
Tian Xiang
In this paper, we study the minimal Keller-Segel model with a logistic source and obtain quantitative and qualitative descriptions of the competition between logistic damping and o…
math.AP2016★ 18 cited
Boundedness and exponential convergence of a chemotaxis model for tumor invasion
Haiyang Jin, Tian Xiang
We revisit the following chemotaxis system modeling tumor invasion \begin{equation*} \begin{cases} u_t=Δu-\nabla \cdot(u\nabla v),& x\inΩ, t>0,\\ v_t=Δv+wz,& x\inΩ, t>0,\\ w_t=-wz,…