Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients
Résumé
We derive global Carleman estimates for one-dimensional linear parabolic equations $\d_t \pm \d_x(c \d_x)$ with a coefficient of bounded variations. These estimates are obtained by approximating $c$ by piecewise constant coefficients, $c_\eps$, and passing to the limit in the Carleman estimates associated to the operators defined with $c_\eps$. Such estimates yields observability inequalities for the considered linear parabolic equation, which, in turn, yield controllability results for classes of semi-linear equations.
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