A variational principle for gradient flows of nonconvex energies

We present a variational approach to gradient ows of energies of the form  E = ø₁ – ø₂  where ø₁ – ø₂  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 λ-convex energies E. The application of the abstract theory to classes of nonlinear parabolic equations with nonmonotone nonlinearities is presented.