On the obstacle problem for fractional semilinear wave equations

2020/11/04 by Mauro Bonafini, Van Phu Cuong Le, Bonafini, Mauro +5
Mathematics · #35L15(Secondary) #35L86(Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2011.02246

26 pages, 2 figures

arxiv created 2021/04/02 · arxiv updated 2021/04/05

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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