Uniqueness of recovery of some systems of semilinear partial differential equations

We prove uniqueness of the term c(x, t, u) of systems of partial differential equations partial derivative (l)u - Deltau + c(x, t, u) = 0 and -Deltau + c(x, u) = 0 with the Dirichlet-to-Neumann map given on a part of the lateral boundary. We use a linearization method, singular solutions in the boundary reconstruction, and almost exponential solutions in the interior reconstruction of the linearized equations.