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arXiv · 2011.02246

On the obstacle problem for fractional semilinear wave equations

Mauro Bonafini·Van Phu Cuong Le·Matteo Novaga·Giandomenico Orlandi
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Abstract

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.

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Mauro Bonafini, Van Phu Cuong Le, Matteo Novaga, Giandomenico Orlandi. 2020-11-04. On the obstacle problem for fractional semilinear wave equations. https://arxiv.org/abs/2011.02246

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