Type: Article

Stochastic Ginzburg-Landau equation on a half-line driven by the multiplicative noise

Juárez-Campos, B., Kaikina, E. I., Vázquez-Esquivel, A. V.;

Abstract:

We consider the stochastic nonlinear Ginzburg-Landau equations driven by the multiplicative noise on the half-line with Neumann brown-noise boundary conditions. We establish the existence and uniqueness of a solution to an initial-boundary value problem with values in Sobolev space H1. We are also interested in the regularity behavior of the solution, especially near the origin, where the boundary data are highly irregular.