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Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations

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 parabilic equations. Sub-linear and super-linear cases are considered.
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Franck Boyer, Jérôme Le Rousseau. Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2014, 31 (5), pp.1035-1078. ⟨10.1016/j.anihpc.2013.07.011⟩. ⟨hal-00724766⟩

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