{"ID":2832513,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.05606","arxiv_id":"2512.05606","title":"Feedback stabilization of some fourth-order nonlinear parabolic equations with saturated controls","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.","short_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...","url_abs":"https://arxiv.org/abs/2512.05606","url_pdf":"https://arxiv.org/pdf/2512.05606v2","authors":"[\"Patricio Guzmán\",\"Felipe Labra\",\"Hugo Parada\"]","published":"2025-12-05T10:49:31Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.AP\",\"math.OC\"]","methods":"[]","has_code":false}