Abstract

The main goal of this work is to propose a non-Markovian model for a subdiffusive transport of particles with nonlinear interaction that involves adhesion affects on escape rates from position x, in inhomogeneous media. In this case, the escape rates to be dependent on the particle density and also effected by the density at the neighbors as well as the chemotactic gradient. We systematically derive the subdiffusive fractional master equation. Considering the spatial continuum limit of the fractional master equation implies a stationary solution of the resulted fractional subdiffusive master equation. Finally, we analyze the role of adhesion in the resulted stationary density.

摘要

这项工作的主要目的是提出一种非马尔可夫模型，用于在非均匀介质中具有非线性相互作用的，涉及粘附力影响从位置x逸出率的粒子的亚扩散传输。在这种情况下，逃逸速率取决于颗粒密度，并且还受邻近的密度以及趋化梯度的影响。我们系统地导出了亚扩散分数主方程。考虑分数阶主方程的空间连续性极限意味着所得分数阶次扩散主方程的平稳解。最后，我们分析了粘附力在产生的固定密度中的作用。