Boundary null controllability of degenerate heat equation as the limit of internal controllability

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 ((uɛ,hɛ))ɛ>0 solving corresponding singularly perturbed internal null controllability problems. As in other situations stu...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2022-08, Vol.66, p.103519, Article 103519
Main Authors: Araújo, B.S.V., Demarque, R., Viana, L.
Format: Article
Language:English
Subjects:
Asymptotic behavior of solutions to PDEs
Controllability
Degenerate parabolic equations
Heat equation
Observability
Singular perturbations in context of PDEs
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Summary: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 ((uɛ,hɛ))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.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2022.103519