趋化性模型的一个校正解耦格式
A corrected decoupled scheme for chemotaxis models
摘要：
本文的主要目的是提出一个新的校正解耦格式结合空间有限体积法的趋化模型。首先，我们推导了一个胚胎学中的抛物-椭圆趋化模型。然后，我们建立的数值解的存在性和唯一性，我们证明了它收敛到一个相应的弱解的研究模型。在最后一节中，几个数值测试，通过应用我们的方法，一些趋化性系统。数值实验结果表明了该方法的有效性和对不同形式的空间模式的有效性。
英文摘要：
The main purpose of this paper is to present a new corrected decoupled scheme combined with a spatial finite volume method for chemotaxis models. First, we derive the scheme for a parabolic-elliptic chemotaxis model arising in embryology. We then establish the existence and uniqueness of the numerical solution, and we prove that it converges to a corresponding weak solution for the studied model. In the last section, several numerical tests are presented by applying our approach to a number of chemotaxis systems. The obtained numerical results demonstrate the efficiency of the proposed scheme and its effectiveness to capture different forms of spatial patterns.
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