| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 81 | |
| Number of page(s) | 34 | |
| DOI | https://doi.org/10.1051/cocv/2025068 | |
| Published online | 26 September 2025 | |
Stabilization to trajectories of nonisothermal Cahn–Hilliard equations
1
Department of Mathematics and Statistics, University of Konstanz, Universitätsstr. 10, 78457 Konstanz, Germany
2
Johann Radon Institute for Computational and Applied Mathematics, ÖAW, Altenbergerstr. 69, 4040 Linz, Austria
* Corresponding author: sergio.rodrigues@ricam.oeaw.ac.at
Received:
6
November
2024
Accepted:
10
August
2025
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.
Mathematics Subject Classification: 93D15 / 93B52 / 93C20 / 35K52 / 35Q93 / 65M22
Key words: Exponential stabilization to trajectories / Cahn–Hilliard systems / oblique projection feedback / finite-dimensional control
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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