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.

On the obstacle problem for fractional semilinear wave equations

Novaga M.;
2021-01-01

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 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.
2021
Bonafini, M.; Le, V. P. C.; Novaga, M.; Orlandi, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1114514
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