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.
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Keywords: Controllability, heat equation, observability, wave equation, transmutation technique
@article{COCV_2021__27_1_A68_0,
author = {Dard\'e, J\'er\'emi and Ervedoza, Sylvain and Morales, Roberto},
editor = {Buttazzo, G. and Casas, E. and de Teresa, L. and Glowinski, R. and Leugering, G. and Tr\'elat, E. and Zhang, X.},
title = {Uniform null controllability for parabolic equations with discontinuous diffusion coefficients},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021063},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021063/}
}
TY - JOUR AU - Dardé, Jérémi AU - Ervedoza, Sylvain AU - Morales, Roberto ED - Buttazzo, G. ED - Casas, E. ED - de Teresa, L. ED - Glowinski, R. ED - Leugering, G. ED - Trélat, E. ED - Zhang, X. TI - Uniform null controllability for parabolic equations with discontinuous diffusion coefficients JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021063/ DO - 10.1051/cocv/2021063 LA - en ID - COCV_2021__27_1_A68_0 ER -
%0 Journal Article %A Dardé, Jérémi %A Ervedoza, Sylvain %A Morales, Roberto %E Buttazzo, G. %E Casas, E. %E de Teresa, L. %E Glowinski, R. %E Leugering, G. %E Trélat, E. %E Zhang, X. %T Uniform null controllability for parabolic equations with discontinuous diffusion coefficients %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021063/ %R 10.1051/cocv/2021063 %G en %F COCV_2021__27_1_A68_0
Dardé, Jérémi; Ervedoza, Sylvain; Morales, Roberto. Uniform null controllability for parabolic equations with discontinuous diffusion coefficients. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 66. doi: 10.1051/cocv/2021063
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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.
