Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 5, p. 1035-1078

In arbitrary dimension, in the discrete setting of finite-differences we prove a Carleman estimate for a semi-discrete parabolic operator, in which the large parameter is connected to the mesh size. This estimate is applied for the derivation of a (relaxed) observability estimate, that yield some controlability results for semi-linear semi-discrete parabolic equations. Sub-linear and super-linear cases are considered.

DOI : https://doi.org/10.1016/j.anihpc.2013.07.011
Classification:  35K10,  35K58,  65M06,  93B05,  93B07
Keywords: Parabolic operator, Semi-discrete Carleman estimates, Observability, Null controllability, Semi-linear equations
@article{AIHPC_2014__31_5_1035_0,
     author = {Boyer, Franck and Le Rousseau, J\'er\^ome},
     title = {Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {31},
     number = {5},
     year = {2014},
     pages = {1035-1078},
     doi = {10.1016/j.anihpc.2013.07.011},
     zbl = {1302.35081},
     mrnumber = {3258365},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2014__31_5_1035_0}
}
Boyer, Franck; Le Rousseau, Jérôme. Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 5, pp. 1035-1078. doi : 10.1016/j.anihpc.2013.07.011. http://www.numdam.org/item/AIHPC_2014__31_5_1035_0/

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