Pattern formation in 2d stochastic anisotropic Swift-Hohenberg equation
Analysis of PDEs
2022-12-05 v1 Numerical Analysis
Numerical Analysis
Probability
Abstract
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.
Cite
@article{arxiv.2212.00976,
title = {Pattern formation in 2d stochastic anisotropic Swift-Hohenberg equation},
author = {Reika Fukuizumi and Yueyuan Gao and Guido Schneider and Motomitsu Takahashi},
journal= {arXiv preprint arXiv:2212.00976},
year = {2022}
}
Comments
24 pages, 8 figures