Minimizing Movements for Hyperbolic Obstacle-Type Problems and Applications

We survey a number of results obtained in Bonafini, Novaga, and Orlandi (2019), Bonafini et al. (2021), Bonafini and Le (2022) that provide existence of solutions for a wide class of hyperbolic obstacle-type problems, including non local operators as well as vector-valued maps. The main results are obtained through a variational scheme inspired to De Giorgi's minimizing movements. As a first application, a compactness result is derived for energy concentration sets in hyperbolic Ginzburg-Landau models for cosmology. Further applications are given for the description of the dynamics of a string interacting with a rigid substrate through an adhesive layer.