Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients

Abstract

We derive global Carleman estimates for one-dimensional linear parabolic operators ∂ t ± ∂ x ( c ∂ x ) with a coefficient c with bounded variations. These estimates are obtained by approximating c by piecewise regular coefficients, c ε , and passing to the limit in the Carleman estimates associated to the operators defined with c ε . Such estimates yield results of controllability to the trajectories for a class of semilinear parabolic equations. To cite this article: J. Le Rousseau, C. R. Acad. Sci. Paris, Ser. I 344 (2007).