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

Thuy Nguyen (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Mots clés: Parabolic operator-semi-discrete Carleman estimates-non smooth coefficients-observability-null controlability

Domaines: Optimisation et contrôle [math.OC]

Thuy Nguyen. Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and application to controllability. 2012. ⟨hal-00750064⟩