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March  2019, 9(1): 221-222. doi: 10.3934/mcrf.2019006

Erratum on: Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain

Jonathan Touboul

Mathematical Neuroscience Laboratory, CIRB-Collège de France and BANG Laboratory, INRIA Paris-Rocquencourt, 11, place Marcelin Berthelot, 75005 Paris, France

Received  January 2018 Revised  February 2018 Published  August 2018

Keywords: Heat equations, Wave equations, controllability, shape of the domain, semi-discrete controllability.
Mathematics Subject Classification: Primary: 35K05, 93B03; Secondary: 65M06.
Citation: Jonathan Touboul. Erratum on: Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain. Mathematical Control & Related Fields, 2019, 9 (1) : 221-222. doi: 10.3934/mcrf.2019006
References:
[1]

K. Beauchard, Local controllability of a 1-d schrödinger equation, Journal de Mathématiques Pures et Appliquées, 84 (2005), 851-956.  doi: 10.1016/j.matpur.2005.02.005.  Google Scholar

[2]

H. Brezis, Analyse Fonctionnelle: Théorie et Applications, Masson, Paris, France, 1983.  Google Scholar

[3]

J. Lohéac, E. Trélat and E. Zuazua, Minimal controllability time for the heat equation under unilateral state or control constraints, 2017. Google Scholar

[4]

I. Moyano, Controllability of a 2d quantum particle in a time-varying disc with radial data, Journal of Mathematical Analysis and Applications, 455 (2017), 1323-1350.  doi: 10.1016/j.jmaa.2017.05.002.  Google Scholar

[5]

Y. Privat, E. Trélat and E. Zuazua, Optimal observation of the one-dimensional wave equation, Journal of Fourier Analysis and Applications, 19 (2013), 514-544.  doi: 10.1007/s00041-013-9267-4.  Google Scholar

[6]

J. Touboul, Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain, Mathematical Control and Related Fields, 2 (2013), 429-455.  doi: 10.3934/mcrf.2012.2.429.  Google Scholar

[7]

E. Trélat, C. Zhang and E. Zuazua, Optimal shape design for 2D heat equations in large time, arXiv preprint, arXiv: 1705.02764, 2017. Google Scholar

show all references

References:
[1]

K. Beauchard, Local controllability of a 1-d schrödinger equation, Journal de Mathématiques Pures et Appliquées, 84 (2005), 851-956.  doi: 10.1016/j.matpur.2005.02.005.  Google Scholar

[2]

H. Brezis, Analyse Fonctionnelle: Théorie et Applications, Masson, Paris, France, 1983.  Google Scholar

[3]

J. Lohéac, E. Trélat and E. Zuazua, Minimal controllability time for the heat equation under unilateral state or control constraints, 2017. Google Scholar

[4]

I. Moyano, Controllability of a 2d quantum particle in a time-varying disc with radial data, Journal of Mathematical Analysis and Applications, 455 (2017), 1323-1350.  doi: 10.1016/j.jmaa.2017.05.002.  Google Scholar

[5]

Y. Privat, E. Trélat and E. Zuazua, Optimal observation of the one-dimensional wave equation, Journal of Fourier Analysis and Applications, 19 (2013), 514-544.  doi: 10.1007/s00041-013-9267-4.  Google Scholar

[6]

J. Touboul, Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain, Mathematical Control and Related Fields, 2 (2013), 429-455.  doi: 10.3934/mcrf.2012.2.429.  Google Scholar

[7]

E. Trélat, C. Zhang and E. Zuazua, Optimal shape design for 2D heat equations in large time, arXiv preprint, arXiv: 1705.02764, 2017. Google Scholar

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