Boundary null controllability of a class of 2-d degenerate parabolic PDEs
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 -dimensional domains, and potential extensions and open problems are discussed to motivate further research in this area.
Keywords
Cite
@article{arxiv.2412.08767,
title = {Boundary null controllability of a class of 2-d degenerate parabolic PDEs},
author = {Víctor Hernández-Santamaría and Subrata Majumdar and Luz de Teresa},
journal= {arXiv preprint arXiv:2412.08767},
year = {2025}
}