The Mean-Field Limit for Hybrid Models of Collective Motions with Chemotaxis
The Mean-Field Limit for Hybrid Models of Collective Motions with Chemotaxis
复制标题
趋化性集体运动混合模型的平均场极限
DOI：
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复制
发表时间：
2021
影响因子：
2
通讯作者：
T. Paul
中科院分区：
文献类型：
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作者：
R. Natalini;T. Paul
在本文中，我们研究了一般类的混合数学模型的集体运动的细胞化学刺激的影响下。该模型是混合的意义上说，细胞是离散的实体给出的ODE，而化学引诱物被认为是一个连续的信号，解决了扩散方程。对于这个模型，我们证明了平均场的限制在Wasserstein距离的一个系统的耦合的Vlasov型方程的化学吸引方程。我们的方法和结果不是基于经验的措施，而是大量的个人密度的边缘，我们显示的限制与明确的界限，也证明存在性和唯一性的极限系统。在单动力学情形下，我们得到了新的具有趋化性的无压非局部欧拉模型。
In this paper we study a general class of hybrid mathematical models of collective motions of cells under the influence of chemical stimuli. The models are hybrid in the sense that cells are discrete entities given by ODE, while the chemoattractant is considered as a continuous signal which solves a diffusive equation. For this model we prove the mean-field limit in the Wasserstein distance to a system given by the coupling of a Vlasov-type equation with the chemoattractant equation. Our approach and results are not based on empirical measures, but rather on marginals of large number of individuals densities, and we show the limit with explicit bounds, by proving also existence and uniqueness for the limit system. In the monokinetic case we derive new pressureless nonlocal Euler-type model with chemotaxis.