Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and application to controllability
نویسندگان
چکیده
In the discrete setting of one-dimensional finite-differences we prove a Carleman estimate for a semi-discretization of the parabolic operator ∂t − ∂x(c∂x) where the diffusion coefficient c has a jump. As a consequence of this Carleman estimate, we deduce consistent nullcontrollability results for classes of semi-linear parabolic equations.
منابع مشابه
Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations
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-line...
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