Work

Null-controllability for a fourth order parabolic equation under general boundary conditions

Year: 2025

Type: article

Abstract: In this paper, we consider a fourth-order inner-controlled parabolic equation on an open bounded subset of $ {\mathbb{R}}^d $, or a smooth compact manifold with boundary, along with general boundary operators fulfilling the Lopatinskiĭ-Šapiro condition. We derive a spectral inequality for the solution of the parabolic system that yields a null-controllability result. The spectral inequality is a consequence of an interpolation inequality obtained via a Carleman inequality for the bi-Laplace operator under the considered boundary conditions.

Source: Mathematical Control and Related Fields

DOI: 10.3934/mcrf.2025045

Authors: Emmanuel Zongo, Luc Robbiano

Institutions: Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4413208778

FWCI:

Cites: 10

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Related to: 10