  In this paper, we study a mixed variational problem subject to perturbations,
where the noise term is modelled by means of a bilinear form that has to be
understood to be "small" in some sense. Indeed, we consider a family of such
problems and provide a result that guarantees existence and uniqueness of the
solution. Moreover, a stability condition for the solutions yields a
Generalized Collage Theorem, which extends previous results by the same
authors. We introduce the corresponding Galerkin method and study its
convergence. We also analyze the associated inverse problem and we show how to
solve it by means of the mentioned Generalized Collage Theorem and the use of
adequate Schauder bases. Numerical examples show how the method works in a
practical context.
