On the obstacle problem for fractional semilinear wave equations
Mauro Bonafini (1), Van Phu Cuong Le (2), Matteo Novaga (3), and, Giandomenico Orlandi (4) ((1) Institut f\"ur Informatik,, Georg-August-Universit\"at G\"ottingen, (2) University of Trento, (3), University of Pisa, (4) University of Verona)
TL;DR
This paper establishes the existence of weak solutions for the obstacle problem in fractional semilinear wave equations using an approximation scheme, and analyzes the compactness of concentration sets in singular limits.
Contribution
It extends previous linear results to the nonlinear fractional case and introduces a new approximation approach for solving the obstacle problem.
Findings
Existence of weak solutions for fractional semilinear wave obstacle problems.
Compactness properties of concentration sets in singular limits.
Extension of linear case results to nonlinear fractional equations.
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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