A variational principle for gradient flows of nonconvex energies

We present a variational approach to gradient flows of energies of the form E = phi(1) - phi(2) where phi(1), phi(2) are convex functionals on a Hilbert space. A global parameter-dependent functional over trajectories is proved to admit minimizers. These minimizers converge up to subsequences to gradient-flow trajectories as the parameter tends to zero. These results apply in particular to the case of non lambda-convex energies E. The application of the abstract theory to classes of nonlinear parabolic equations with nonmonotone nonlinearities is presented.