论文标题
2D随机各向异性Swift-Hohenberg方程中的图案形成
Pattern formation in 2d stochastic anisotropic Swift-Hohenberg equation
论文作者
论文摘要
在本文中，我们研究了一个现象学模型，用于电射感染中的模式形成以及噪声对模式的影响。因此，我们考虑了各向异性的Swift-Hohenberg方程，并增加了添加噪声。我们证明了该方程式在两个维圆环上的全局解决方案的存在。此外，插入缩放参数，我们考虑了在稳定性变化附近的大域上的方程式。我们从数字上观察到，在适当的缩放率下，可以通过周期性波来近似其溶液，该溶液通过随机Ginzburg-landau方程的溶液调节。
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.
