Nonlinear Waves and Polarization in Diffusive Directed Particle Flow
Nonlinear Waves and Polarization in Diffusive Directed Particle Flow
复制标题
扩散定向粒子流中的非线性波和偏振
DOI：
10.1137/17m1124103
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
J. Fuhrmann
中科院分区：
文献类型：
--
作者：
H. Freistühler;J. Fuhrmann
本文考虑一个由两个反应-扩散-平流方程组成的系统，描述了粒子在扩散和相互排列的情况下的一维定向运动。对于这个系统，我们证明了行波解的存在性弱扩散的奇异摄动技术，并提供证据证明他们的存在性也较强的扩散。我们讨论了不同类型的波前和它们的组成更复杂的模式，并说明了它们的出现，从通用的初始数据模拟。我们还研究了波速对模型参数的依赖关系。
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave solutions for weak diffusion by singular perturbation techniques and provide evidence for their existence also for stronger diffusion. We discuss different types of wave fronts and their composition to more complex patterns and illustrate their emergence from generic initial data by simulations. We also investigate the dependence of the wave velocities on the model parameters.