具有对齐和反转的粘细菌运动动力学模型弱解的存在性
Existence of weak solutions for the kinetic models of motion of myxobacteria with alignment and reversals
AI总结：
本文研究了模拟粘细菌等杆状细胞运动的三个非线性动力学偏微分方程，通过应用经典平均引理及引入单向扩散算子的新版本，证明了这些包含对齐、反转和趋化输运的方程弱解的存在性。
摘要：
本文考虑了在模拟粘细菌等杆状细胞运动时出现的三个非线性动力学偏微分方程。该运动特征为与邻近细胞的向列对齐、细胞极性切换引起的取向反转、取向扩散及趋化驱动的输运。我们的主要贡献在于建立这些方程弱解的存在性。分析方法基于动力学理论中经典平均引理的应用，并结合了一个新颖版本，其中输运算子被单向扩散算子替代。
英文摘要：
In this paper, we consider three non-linear kinetic partial differential equations that emerge in the modeling of motion of rod-shaped cells such as myxobacteria. This motion is characterized by nematic alignment with neighboring cells, orientation reversals from cell polarity switching, orientation diffusion, and transport driven by chemotaxis. Our primary contribution lies in establishing the existence of weak solutions for these equations. Our analytical approach is based on the application of the classical averaging lemma from the kinetic theory, augmented by a novel version where the transport operator is substituted with a uni-directional diffusion operator.
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