  A system of two operator equations is considered - one of pseudomonotone type
and the other of strongly monotone type - both being strongly coupled.
Conditions are given that allow to reduce the solvability of this system to a
single operator equation for a pseudomonotone mapping. This result is applied
to a coupled system consisting of a parabolic equation of forth order in space
of Cahn-Hilliard type and a nonlinear elliptic equation of second order to a
quasi-steady mechanical equilibrium. Using an appropriate notation of weak
solutions and a framework for evolution equations developed by Gr\"oger, the
system is reduced to a single parabolic operator equation and the existence of
solutions are shown under restrictions on the strength of the coupling.
