In this paper, we study a phenomenological model for pattern formation in electroconvection, and the effect of noise on the pattern. As such model we consider an anisotropic Swift-Hohenberg equation adding an additive noise. We prove the existence of a global solution of that equation on the two dimensional torus. In addition, inserting a scaling parameter, we consider the equation on a large domain near its change of stability. We observe numerically that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation.
翻译:在本文中,我们研究了电对等中模式形成模式的血球学模型,以及噪音对模式的影响。作为模型,我们考虑的是一种厌食性斯威夫特-霍亨贝格方程式,增加了一种添加噪音。我们证明在二维横线上存在一种该方程式的全球解决办法。此外,我们插入一个缩放参数,我们考虑在一个大领域上接近稳定性变化的方程式。我们从数字上观察,在适当的缩放下,其解决方案可以用一个周期波相近,而周期波则由一个随机的甘斯堡-兰道方程式的解决方案来调节。