no. 5
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) no. 5, pp. 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 : 10.1016/j.anihpc.2013.07.011
Classification : 35K10, 35K58, 65M06, 93B05, 93B07
Mots clés : Parabolic operator, Semi-discrete Carleman estimates, Observability, Null controllability, Semi-linear equations 
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     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},
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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) 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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