A Chemotaxis Model with Threshold Density and Degenerate Diffusion
A Chemotaxis Model with Threshold Density and Degenerate Diffusion
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DOI：
10.1007/3-7643-7385-7_16
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发表时间：
2005
影响因子：
2.9
通讯作者：
P. Laurençot;D. Wrzosek
中科院分区：
文献类型：
--
作者：
P. Laurençot;D. Wrzosek
研究了模拟细胞趋化运动的拟线性退化抛物系统。所考虑的系统具有与经典Keller-Segel模型相似的结构，但具有以下特点：存在一个细胞密度不能超过的阈值，当细胞密度达到该阈值时，细胞的流量为零。证明了弱解的存在唯一性。在一维情形下，构造了平坦驼峰形的定常解。
A quasilinear degenerate parabolic system modelling the chemotactic movement of cells is studied. The system under consideration has a similar structure as the classical Keller-Segel model, but with the following features: there is a threshold value which the density of cells cannot exceed and the flux of cells vanishes when the density of cells reaches this threshold value. Existence and uniqueness of weak solutions are proved. In the one-dimensional case, flat-hump-shaped stationary solutions are constructed.