JournalsaihpcVol. 31, No. 5pp. 1035–1078

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

  • Franck Boyer

    Aix-Marseille Université, Laboratoire d'Analyse Topologie Probabilités (LATP), CNRS UMR 7353, 39 rue F. Joliot-Curie, 13453 Marseille cedex 13, France
  • Jérôme Le Rousseau

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

Cite this article

Franck Boyer, Jérôme Le Rousseau, Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 5, pp. 1035–1078

DOI 10.1016/J.ANIHPC.2013.07.011