Work

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

Year: 2025

Type: article

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 degeneracy occurs. Furthermore, we establish a Kalman rank condition as a full characterization of boundary controllability for coupled degenerate systems. The results are extended to $ N $-dimensional domains, and some other potential extensions, along with open problems, are discussed to motivate further research in this area.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025084

Authors: Víctor Hernández-Santamaría, Subrata Majumdar, Luz de Teresa

Institution: Universidad Nacional Autónoma de México

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funder: Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México

Award: G629546816