等离子体中带有交叉扩散的反应-扩散模型的图灵不稳定性和行波（英文）  

Turing instability and traveling fronts for a reaction-diffusion model with cross-diffusion in plasmas

作　　者：凌赫阳 彭亚红 

机构地区：[1]东华大学理学院,上海201620

出　　处：《纺织高校基础科学学报》2017年第3期318-324,330,共8页Basic Sciences Journal of Textile Universities

基　　金：Supported by the National Natural Science Foundation of China(11571227)

摘　　要：磁约束等离子体中湍流、剪切流相互作用的模型得到了广泛研究,其中图灵斑图的形成成为研究重点.本文研究交叉扩散对一类磁约束等离子体模型的影响.首先通过线性化分析,研究了系统平衡点的稳定性,发现交叉扩散是导致斑图形成的关键因素.其次,通过将时间、空间尺度展开成快慢尺度后,用弱的非线性分析的方法,得到斑图的振幅方程由实Ginzburg-Landau方程确定.The model of turbulence shear flow interaction has been widely studied in the magnetically confined plasmas,and an important problem is to understand how Turing pattern forms.The influence of cross-diffusion on a magnetically confined plasmas model is concerned.Stability at the equilibrium points are analyzed by linear analysis,it is shown that the diffusion term is the key mechanism of pattern formation.Then through the expansion of multiple scales,time scale and spatial scale are separated into fast scale and slow scale.The result of weakly nonlinear analysis indicates that the solution of real Ginzburg-Landau equation describes the amplitude equation.

关 键 词：反应-扩散 图灵失稳 振幅方程 弱非线性展开 行波 等离子体 

分 类 号：O175.26[理学—数学]