Local null controllability of a cubic Ginzburg-Landau equation with dynamic boundary conditions

This paper deals with controllability properties of a cubic Ginzburg-Landau equation with dynamic boundary conditions. More precisely, we prove a local null controllability result by using a single control supported in a small subset of the domain. In order to achieve this result, we firstly linearize the system around the origin and we analyze it by the duality approach and an appropriate Carleman estimate. Then, by using an inverse function theorem, the local null controllability of the nonlinear system is proven.