# American Institute of Mathematical Sciences

June  2014, 4(2): 203-259. doi: 10.3934/mcrf.2014.4.203

## Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and applications to controllability

 1 Université d'Orléans, Bâtiment de Mathématiques (MAPMO), B.P. 6759, 45067 Orléans cedex 2, France

Received  January 2013 Revised  July 2013 Published  February 2014

In the discrete setting of one-dimensional finite-differences we prove a Carleman estimate for a semi-discretization of the parabolic operator $\partial_t-\partial_x (c\partial_x )$ where the diffusion coefficient $c$ has a jump. As a consequence of this Carleman estimate, we deduce consistent null-controllability results for classes of semi-linear parabolic equations.
Citation: Thuy N. T. Nguyen. Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and applications to controllability. Mathematical Control & Related Fields, 2014, 4 (2) : 203-259. doi: 10.3934/mcrf.2014.4.203
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