Inserted: 4 nov 2020
Last Updated: 27 apr 2021
Journal: Nonlinear Analysis
We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in 9, where the linear case was treated. In addition, we deduce some compactness properties of concentration sets (e.g. moving interfaces) when dealing with singular limits of certain nonlinear wave equations.
Keywords: minimizing movements, Hyperbolic obstacle problem, Non-local nonlinear wave equations