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 Bonafini et al. (2019), 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.

中文翻译：

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分数阶半线性波动方程的障碍问题

我们本着最小化运动的精神，通过使用一种合适的逼近方案，证明了半线性波动方程（包括分数情形）的障碍问题的弱解的存在。这扩展了Bonafini等人的结果。（2019），其中对线性案例进行了处理。此外，当处理某些非线性波动方程的奇异极限时，我们推导了浓度集（例如移动界面）的一些紧性。