Controlling linear and semilinear systems formed by one elliptic and two parabolic PDEs with one scalar control
ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 4, pp. 1017-1039.

In this paper, we prove controllability results for some linear and semilinear systems where we find two parabolic PDEs and one elliptic PDE and we act through one locally supported in space scalar control. The arguments rely on a careful analysis of the linear case and an application of an inverse function theorem. The facts that we act through a single scalar control and one of the PDEs has no time derivative are the main novelties and introduce several nontrivial difficulties.

Received:
Accepted:
DOI: 10.1051/cocv/2016031
Classification: 35B37, 35A05, 35B40
Mots-clés : Null controllability, parabolic-elliptic linear and semilinear systems, Carleman estimates
Fernández-Cara, E. 1; Limaco, J. 2; de Menezes, S. B. 3

1 Dpto. EDAN e IMUS, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain.
2 Inst. Matemática, Universidade Federal Fluminense, Valonguinho, 24020-140, Niterói, RJ, Brasil.
3 Dpto. Matemática, Universidade Federal do Ceará, Campus do Pici – Bloco 914, 60455-760, Fortaleza, CE, Brasil.
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     title = {Controlling linear and semilinear systems formed by one elliptic and two parabolic {PDEs} with one scalar control},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1017--1039},
     publisher = {EDP-Sciences},
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Fernández-Cara, E.; Limaco, J.; de Menezes, S. B. Controlling linear and semilinear systems formed by one elliptic and two parabolic PDEs with one scalar control. ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 4, pp. 1017-1039. doi : 10.1051/cocv/2016031. http://archive.numdam.org/articles/10.1051/cocv/2016031/

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