Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding
Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding
复制标题
DOI：
10.1006/aama.2001.0721
复制
发表时间：
2001-05
期刊：
影响因子：
--
通讯作者：
T. Hillen;K. Painter
中科院分区：
文献类型：
--
作者：
T. Hillen;K. Painter
本文研究了一类Keller-Segel模型，其中趋化交叉扩散同时依赖于外部信号和局部种群密度。然后是一个抛物型拟线性强耦合系统。通过引入群体感应(或“群体感应”)机制，我们假设趋化反应在高细胞密度时被关闭。对高人口密度的反应防止了过度拥挤，我们证明了经典解的局部和全局存在性。数值模拟显示了图案形成和稳定聚集体形成的有趣现象。我们讨论了与以前关于Keller-Segel模型的分析结果相关的结果。
In this paper we study a version of the Keller-Segel model where the chemotactic cross-diffusion depends on both the external signal and the local population density. A parabolic quasi-linear strongly coupled system follows. By incorporation of a population-sensing (or ''quorum-sensing'') mechanism, we assume that the chemotactic response is switched off at high cell densities. The response to high population densities prevents overcrowding, and we prove local and global existence in time of classical solutions. Numerical simulations show interesting phenomena of pattern formation and formation of stable aggregates. We discuss the results with respect to previous analytical results on the Keller-Segel model.