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.
@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}, volume = {31}, year = {2014}, pages = {1035-1078}, doi = {10.1016/j.anihpc.2013.07.011}, mrnumber = {3258365}, zbl = {1302.35081}, language = {en}, url = {http://dml.mathdoc.fr/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, Tome 31 (2014) pp. 1035-1078. doi : 10.1016/j.anihpc.2013.07.011. http://gdmltest.u-ga.fr/item/AIHPC_2014__31_5_1035_0/
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