Boundary null controllability of a class of 2-d degenerate parabolic PDEs

2024/12/11 by Víctor Hernández-Santamaría, Hernández-Santamaría, Víctor, Subrata Majumdar +3 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2412.08767

openalex publication_date 2024/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article deals with the boundary null controllability of some degenerate parabolic equations posed on a square domain, presenting the first study of boundary controllability for such equations in multidimensional settings. The proof combines two classical techniques: the method of moments and the Lebeau-Robbiano strategy. A key novelty of this work lies in the analysis of boundary control localized on a subset of the boundary where the degeneracy occurs. Furthermore, we establish the Kalman rank condition as a full characterization of boundary controllability for coupled degenerate systems. The results are extended to N-dimensional domains, and potential extensions and open problems are discussed to motivate further research in this area.

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• On the controllability of the Kuramoto-Sivashinsky equation on multi-dimensional cylindrical domains

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