Calculus of Variations and Geometric Measure Theory
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M. Bonafini - V. P. C. Le - M. Novaga - G. Orlandi

On the obstacle problem for fractional semilinear wave equations

created by le on 04 Nov 2020
modified by novaga on 27 Apr 2021


Published Paper

Inserted: 4 nov 2020
Last Updated: 27 apr 2021

Journal: Nonlinear Analysis
Volume: 210
Number: 112368
Year: 2021

ArXiv: 2011.02246 PDF


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.

Keywords: minimizing movements, Hyperbolic obstacle problem, Non-local nonlinear wave equations


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