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arXiv · 2512.05606

Feedback stabilization of some fourth-order nonlinear parabolic equations with saturated controls

Patricio Guzmán·Felipe Labra·Hugo Parada
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Abstract

In this work, we analyze the internal and boundary stabilization of the Cahn-Hilliard and Kuramoto-Sivashinsky equations under saturated feedback control. We conduct our study through the spectral analysis of the associated linear operator. We identify a finite number of eigenvalues related to the unstable part of the system and then design a stabilization strategy based on modal decomposition, linear matrix inequalities (LMIs), and geometric conditions on the saturation function. Local exponential stabilization in $H^{2}$ is established.

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Patricio Guzmán, Felipe Labra, Hugo Parada. 2025-12-05. Feedback stabilization of some fourth-order nonlinear parabolic equations with saturated controls. https://arxiv.org/abs/2512.05606

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