@article {PSR1-15, title = {A variational principle for gradient flows of nonconvex energies}, number = {1PV15/0/0}, year = {2015}, month = {12 april 2015}, pages = {23}, publisher = {CNR-IMATI}, type = {Working paper}, chapter = {Serie Rossa}, address = {Pavia}, abstract = {

We present a variational approach to gradient ows of energies of the form \ E = {\o}1 {\textendash} {\o}2 \ where\ {\o}1 {\textendash} {\o}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 λ-convex energies E. The application of the abstract theory to classes of nonlinear parabolic equations with nonmonotone nonlinearities is presented.

}, keywords = {Evolution equations, Gradient flow, Nonconvex energy, Variational formulation}, issn = {1722-8964}, url = {http://archives.imati.cnr.it/publ-r/1PV15}, author = {G. Akagi and U. Stefanelli} }