Global null controllability of stochastic semilinear complex Ginzburg-Landau equations

TL;DR

This paper establishes the global null controllability of stochastic semilinear complex Ginzburg-Landau equations using advanced Carleman estimates and fixed point techniques, advancing control theory for complex stochastic PDEs.

Contribution

It introduces improved global Carleman estimates for linear systems and applies a fixed point approach to achieve null controllability for semilinear stochastic equations.

Findings

Proved null controllability for stochastic linear systems with $L^2$-valued sources.

Extended controllability results to semilinear systems with Lipschitz nonlinearities.

Developed new Carleman estimates for complex Ginzburg-Landau equations.

Abstract

In this paper, we study the null controllability of forward and backward stochastic semilinear complex Ginzburg-Landau equations with global Lipschitz nonlinear terms. For this purpose, by deriving an improved global Carleman estimates for linear systems, we obtain the controllability results for the stochastic linear systems with a $L^2$-valued source term. Based on it, together with a Banach fixed point argument, the desired null controllability of semilinear systems is derived.