Stably determining time-dependent convection–diffusion coefficients from a partial Dirichlet-to-Neumann map

Abstract

Abstract We study in this paper the inverse problem for the dynamical convection–diffusion equation. More precisely, we set logarithmic stability estimates in the determination of the two time-dependent first-order convection term and the scalar potential appearing in the heat equation. The observations here are taken only on an arbitrary open subset of the boundary and are given by a partial Dirichlet-to-Neumann map. For this end, we will reduce our initial problem into an auxiliary one then we will construct particular solutions and apply a special parabolic Carleman estimate.