We investigate the well-posedness of the recently proposed Cahn-Hilliard-Biot
model. The model is a three-way coupled PDE of elliptic-parabolic nature, with
several nonlinearities and the fourth order term known to the Cahn-Hilliard
system. We show existence of weak solutions to the variational form of the
equations and uniqueness under certain conditions of the material parameters
and secondary consolidation, adding regularizing effects. Existence is shown by
discretizing in space and applying ODE-theory (the Peano-Cauchy theorem) to
prove existence of the discrete system, followed by compactness arguments to
retain solutions of the continuous system. In addition, the continuous
dependence of solutions on the data is established, in particular implying
uniqueness. Both results build strongly on the inherent gradient flow structure
of the model