Pré-Publication, Document De Travail Année : 2025

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

Résumé

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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Dates et versions

hal-05398937 , version 1 (04-12-2025)
hal-05398937 , version 2 (18-12-2025)

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  • HAL Id : hal-05398937 , version 2

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Patricio Guzmán, Felipe Labra, Hugo Parada. Feedback stabilization of some fourth-order nonlinear parabolic equations with saturared controls. 2025. ⟨hal-05398937v2⟩
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