Optimal decay rates for a chemotaxis model with logistic growth, logarithmic sensitivity and density-dependent production/consumption rate
Optimal decay rates for a chemotaxis model with logistic growth, logarithmic sensitivity and density-dependent production/consumption rate
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DOI：
10.1016/j.jde.2019.08.050
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发表时间：
2020-02
影响因子：
2.4
通讯作者：
Yanni Zeng;Kun Zhao
中科院分区：
文献类型：
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作者：
Yanni Zeng;Kun Zhao
摘要考虑一类具有对数灵敏度和密度依赖的生产/消费率的Logistic增长的Keller-Segel型趋化模型。它是一个2× 2的反应扩散系统，描述了细胞和化学信号的相互作用。研究原系统及其变换系统的Cauchy问题，这是一个双曲-抛物平衡律。我们的初始数据是一个恒定的基态的一般扰动，即扰动的初始质量是非零的。在非扩散化学的情况下，我们得到了最佳的L2时间衰减率的解决方案与有限的初始数据。在扩散化学的情况下，最佳的L2速率也得到了额外的假设上的初始振幅小，但仍然允许大的振荡。
Abstract We consider a Keller-Segel type chemotaxis model with logistic growth, logarithmic sensitivity and density-dependent production/consumption rate. It is a 2× 2 reaction-diffusion system describing the interaction of cells and a chemical signal. We study Cauchy problem for the original system and its transformed system, which is one of hyperbolic-parabolic balance laws. Our initial data are generic perturbations of a constant ground state, ie the initial mass of perturbation is non-zero. In the case of non-diffusive chemical, we obtain optimal L 2 time decay rates for the solution with finite initial data. In the case of diffusive chemical, optimal L 2 rates are also obtained with additional assumption on the smallness of the initial amplitude but still allowing large oscillation.