Volpert V A, Kanevsky Y, Nepomnyashchy A A
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208-3100, USA.
Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000 Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):012901. doi: 10.1103/PhysRevE.89.012901. Epub 2014 Jan 3.
The propagation of subdiffusion-reaction fronts is studied in the framework of a model recently suggested by Fedotov [ Phys. Rev. E 81 011117 (2010)]. An exactly solvable model with a piecewise linear reaction function is considered. A drastic difference between the cases of normal diffusion and subdiffusion has been revealed. While in the case of normal diffusion, a traveling wave solution between two locally stable phases always exists, and is unique, in the case of the subdiffusion such solutions do not exist. The numerical simulation shows that the velocity of the front decreases with time according to a power law. The only kind of fronts moving with a constant velocity are waves which propagate solely due to the reaction, with a vanishing subdiffusive flux.
在费多托夫最近提出的一个模型框架内（《物理评论E》81 011117 (2010)），研究了亚扩散 - 反应前沿的传播。考虑了一个具有分段线性反应函数的精确可解模型。揭示了正常扩散和亚扩散情况之间的巨大差异。在正常扩散情况下，两个局部稳定相之间总是存在且唯一存在行波解，而在亚扩散情况下不存在此类解。数值模拟表明，前沿速度随时间按幂律下降。唯一以恒定速度移动的前沿类型是仅由反应驱动传播且亚扩散通量消失的波。
