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We investigate a variational approach to nonpotential perturbations ofgradient flows of nonconvex energies in Hilbert spaces. We prove existence ofsolutions to elliptic-in-time regularizations of gradient flows by combiningthe minimization of a parameter-dependent functional over entire trajectoriesand a fixed-point argument. These regularized solutions converge up tosubsequence to solutions of the gradient flow as the regularization parametergoes to zero. Applications of the abstract theory to nonlinearreaction-diffusion systems are presented.

A variational principle for nonpotential perturbations of gradient flows of nonconvex energies