Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations |
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| Authors: | Franck Boyer Jérôme Le Rousseau |
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| Institution: | 1. Aix-Marseille Université, Laboratoire d''Analyse Topologie Probabilités (LATP), CNRS UMR 7353, 39 rue F. Joliot-Curie, 13453 Marseille cedex 13, France;2. Université d''Orléans, Laboratoire de Mathématiques – Analyse, Probabilités, Modélisation – Orléans (MAPMO), CNRS UMR 7349, Fédération Denis Poisson, CNRS FR 2964, B.P. 6759, 45067 Orléans cedex 2, France |
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| Abstract: | 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. |
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| Keywords: | 35K10 35K58 65M06 93B05 93B07 |
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