# A variational scheme for hyperbolic obstacle problems

## TL;DR

This paper introduces a variational method for solving hyperbolic obstacle problems, including non-local wave equations, using a convex minimization approach with a discrete approximation scheme, and discusses numerical implementation and open questions.

## Contribution

It presents a novel variational scheme for hyperbolic obstacle problems, extending to non-local wave equations, with a new numerical implementation method.

## Key findings

- Existence of weak solutions proved.
- Numerical implementation demonstrated.
- Open questions for future research raised.

## Abstract

We consider an obstacle problem for (possibly non-local) wave equations, and we prove existence of weak solutions through a convex minimization approach based on a time discrete approximation scheme. We provide the corresponding numerical implementation and raise some open questions.