On the obstacle problem for fractional semilinear wave equations. (September 2021)

• Record Type: Journal Article
• Authors: Bonafini, M.; Le, V.P.C.; Novaga, M.; Orlandi, G.
• Is Part Of: Nonlinear analysis. Volume 210(2021)
• Publication Date: 2021-09
• Subjects: Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112368
• Languages: English
• ISSNs: 0362-546X

Abstract

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 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.