Stabilization to trajectories of nonisothermal Cahn-Hilliard equations

TL;DR

This paper proves semiglobal exponential stabilization of nonisothermal Cahn-Hilliard equations to time-dependent trajectories using explicit feedback controls with numerical validation.

Contribution

It introduces a novel feedback control method involving oblique projections for stabilizing nonisothermal Cahn-Hilliard systems.

Findings

Successful stabilization demonstrated through numerical simulations.

Feedback operators effectively stabilize the system to desired trajectories.

Results extend to isothermal Cahn-Hilliard equations.

Abstract

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.