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

Abstract

We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time regularizations of gradient flows by combining the minimization of a parameter-dependent functional over entire trajectories and a fixed-point argument. These regularized solutions converge up to subsequences to solutions of the gradient flow as the regularization parameter goes to zero. Applications of the abstract theory to nonlinear reaction–diffusion systems are presented.