DEGENERATE/SINGULAR BEAM-TYPE EQUATIONS: A CONTROLLABILITY RESULT

Akil M. Fragnelli G. Sbai A.
15 December 2026 American Institute of Mathematical Sciences

Mathematical Control and Related Fields
2026 #18 397 - 432 pp.

The paper deals with the controllability of a degenerate/singular beam-type equation in divergence or non-divergence forms. In particular, we assume that the degeneracy and singularity are at the same boundary point, and we consider a suitable control f localized on the non-degenerate boundary point. As a first step, we prove the existence of a solution for the homogeneous problems, then we prove some estimates on their energies. Based on them, we prove two observability inequalities and, using the notion of solution by transposition, we prove that the initial problems are null controllable.

Boundary controllability , degenerate beam equations , observability , singular potentials

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Université Polytechnique Hauts-de-France, INSA Hauts-de-France, CÉRAMATHS-Laboratoire de Matériaux Céramiques et de Mathématiques, Valenciennes, 59313, France
Dipartimento di Ingeneria dell’Informazione e Scienze Matematiche, Università degli Studi di Siena, Via Roma 56, Siena, 53100, Italy
SDU University, Mathematics Department, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

Université Polytechnique Hauts-de-France
Dipartimento di Ingeneria dell’Informazione e Scienze Matematiche
SDU University
Institute of Mathematics and Mathematical Modeling

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