Carleman estimates for semi-discrete parabolic operators with a   discontinuous diffusion coefficient and application to controllability
  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. 
Thuy Nguyen (MAPMO)
math.OC math.AP