Stabilization to trajectories of nonisothermal Cahn–Hilliard equations

In this work, it is proven the semiglobal exponential stabilization to time-dependent trajectories of the nonisothermal Cahn–Hilliard equations. In the model, the input controls are given by explicit feedback operators that involve appropriate oblique projections. The actuators are given by a finite number of indicator functions. The results also hold for the isothermal Cahn–Hilliard system. Numerical simulations are shown that illustrate the stabilizing performance of the proposed input feedback operators.