On the obstacle problem for fractional semilinear wave equations
Analysis of PDEs
2021-04-05 v2
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.
Cite
@article{arxiv.2011.02246,
title = {On the obstacle problem for fractional semilinear wave equations},
author = {Mauro Bonafini and Van Phu Cuong Le and Matteo Novaga and Giandomenico Orlandi},
journal= {arXiv preprint arXiv:2011.02246},
year = {2021}
}
Comments
26 pages, 2 figures