Pattern Formation in 2D Stochastic Anisotropic Swift–Hohenberg Equation

In this paper, we study a phenomenological model for pattern formation in electroconvection, and the effect of noise on pattern. As such consider an anistropic Swift–Hohenberg equation adding additive noise. We prove existence global solution that two dimensional torus. addition, inserting scaling parameter, large domain near its change stability. observe numerically that, under appropriate scaling, solutions can be approximated by periodic wave, which is modulated to stochastic Ginzburg–Landau equation.