  We investigate the Weighted Energy-Dissipation variational approach to
semilinear gradient flows with state-dependent dissipation. A family of
parameter-dependent functionals defined over entire trajectories is introduced
and proved to admit global minimizers. These global minimizers correspond to
solutions of elliptic-in-time regularizations of the limiting causal problem.
By passing to the limit in the parameter we prove that such global minimizers
converge, up to subsequences, to a solution of the gradient flow.
