Boundary null controllability of degenerate heat equation as the limit of internal controllability. (August 2022)

• Record Type: Journal Article
• Authors: Araújo, B.S.V.; Demarque, R.; Viana, L.
• Is Part Of: Nonlinear analysis. Volume 66(2022)
• Publication Date: 2022-08
• Subjects: Heat equation -- Degenerate parabolic equations -- Controllability -- Observability -- Singular perturbations in context of PDEs -- Asymptotic behavior of solutions to PDEs; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103519
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we recover the boundary null controllability for the degenerate heat equation by analyzing the asymptotic behavior of an eligible family of state-control pairs ( ( u ɛ, h ɛ ) ) ɛ > 0 solving corresponding singularly perturbed internal null controllability problems. As in other situations studied in the literature, our approach relies on Carleman estimates and meticulous weak convergence results. However, for the degenerate parabolic case, some specific trace operator inequalities must be obtained, in order to justify correctly the passage to the limit argument.