Homogenization for stochastic Ginzburg-Landau equation on the half-line with fast boundary fluctuation

Abstract

In this paper, we investigate the homogenization for complex stochastic Ginzburg-Landau equation on the half-line with fast boundary fluctuation. Precisely, we first verify the existence and uniqueness of the mild solution to the initial-boundary problem in a weighted space. Next, we discuss the tightness of the mild solution. Finally, we prove that the mild solution of the original system converges to the mild solution of the homogenized equation in probability, as ε goes to zero.