Carleman estimate for a parabolic equation in a Sobolev space of negative order and its applications (Q2717281)

The authors obtain a Carleman estimate for a second order parabolic equation, when the coefficients are not bounded and the right hand side is taken in \(L^2(0,T;H^{-1}(\Omega))\). Then, some applications are presented: NEWLINENEWLINENEWLINE1) the global exact null-controllability of a semilinear parabolic equation, with a nonlinear term containing first order derivatives,NEWLINENEWLINENEWLINE2) conditional stability in the continuation of the solution andNEWLINENEWLINENEWLINE3) the inverse problem of determining a source term belonging to \(H^{-\ell}(\Omega)\) (with \(0 \leq \ell < 1\)) in a parabolic linear equation. NEWLINENEWLINENEWLINENo proofs are provided for the Carleman estimate and the exact controllability result.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00047].