Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
|Number of page(s)||29|
|Published online||28 June 2021|
Uniform null controllability for parabolic equations with discontinuous diffusion coefficients*
Institut de Mathématiques de Toulouse, UMR 5219 – Université de Toulouse, CNRS – UPS,
2 Institut de Mathématiques de Bordeaux UMR 5251, Université de Bordeaux, Bordeaux INP, CNRS, 33400 Talence, France.
3 Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile.
** Corresponding author: firstname.lastname@example.org
Accepted: 7 June 2021
In this article, we study the null-controllability of a heat equation in a domain composed of two media of different constant conductivities. In particular, we are interested in the behavior of the system when the conductivity of the medium on which the control does not act goes to infinity, corresponding at the limit to a perfectly conductive medium. In that case, and under suitable geometric conditions, we obtain a uniform null-controllability result. Our strategy is based on the analysis of the controllability of the corresponding wave operators and the transmutation technique, which explains the geometric conditions.
Mathematics Subject Classification: 35K10 / 35L10 / 93B05 / 93B07 / 93B17
Key words: Controllability / heat equation / observability / wave equation / transmutation technique
The second author has been supported by the Agence Nationale de la Recherche, Project IFSMACS, grant ANR-15-CE40-0010. The first and second authors have been supported by the CIMI Labex, Toulouse, France, under grant ANR-11-LABX-0040-CIMI and the MATH AmSud program ACIPDE. The third author has been supported by FONDECYT 3200830.
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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