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.
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}, pages = {1035--1078}, publisher = {Elsevier}, volume = {31}, number = {5}, year = {2014}, doi = {10.1016/j.anihpc.2013.07.011}, mrnumber = {3258365}, zbl = {1302.35081}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.07.011/} }
TY - JOUR AU - Boyer, Franck AU - Le Rousseau, Jérôme TI - Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 1035 EP - 1078 VL - 31 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.07.011/ DO - 10.1016/j.anihpc.2013.07.011 LA - en ID - AIHPC_2014__31_5_1035_0 ER -
%0 Journal Article %A Boyer, Franck %A Le Rousseau, Jérôme %T Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 1035-1078 %V 31 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2013.07.011/ %R 10.1016/j.anihpc.2013.07.011 %G en %F 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/articles/10.1016/j.anihpc.2013.07.011/
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