be a bounded domain of
, and fix
. We consider the inverse problem of determining (in some suitable sense) a function
and a vector valued function
\[A\in L^\infty(Q;\mathbb R^n)\]
appearing in a Dirichlet initial-boundary value problem for the parabolic equation
, from observations on
. We consider both results of uniqueness and stability for this problem. Moreover, we apply our result to the recovery of some nonlinear term appearing in a parabolic equation from boundary measurements. This talk is based on a joint work with Mourad Choulli and some work in progress with Pedro Caro.