Weighted Inertia-Dissipation-Energy functionals for semilinear equations

We address a global-in-time variational approach to semilinear PDEs of either parabolic or hyperbolic type by means of the so-called Weighted Inertia-Dissipation-Energy (WIDE) functional In particular, minimizers of the WIDE functional are proved to converge, up to subsequences, to weak solutions of the limiting PDE. This entails the possibility of reformulating the limiting differential problem in terms of convex minimization. The WIDE formalism can be used in order to discuss parameters asymptotics via ?-convergence and is extended to some time-discrete situation as well.