Controllability to the Trajectories of Phase-Field Models by One Control Force

Abstract

In this article, we study the controllability to the trajectories of 2 × 2 nonlinear parabolic systems for control forces acting on a single equation of the system. This result, which in particular applies to Caginalp's phase-field model, actually extends those obtained for the semilinear heat equations. The proof relies on Kakutani's fixed point theorem and makes use of an observability estimate for the associated linearized system.