On the obstacle problem for fractional semilinear wave equations

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 additio...

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Bibliographic Details
Published inNonlinear analysis Vol. 210; p. 112368
Main Authors Bonafini, M., Le, V.P.C., Novaga, M., Orlandi, G.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2021
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Summary: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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2021.112368