Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics. (3rd November 2022)

• Record Type: Journal Article
• Authors: Coclite, Giuseppe Maria; Dipierro, Serena; Fanizza, Giuseppe; Maddalena, Francesco; Valdinoci, Enrico
• Is Part Of: Nonlinearity. Volume 35:Number 11(2022)
• Page Start: 5664
• Page End: 5713
• Publication Date: 2022-11-03
• Subjects: peridynamics -- nonlocal continuum mechanics -- elasticity; 74A70 -- 74B10 -- 70G70 -- 35Q70; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac8fd9
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We study the dispersive properties of a linear equation in one spatial dimension which is inspired by models in peridynamics. The interplay between nonlocality and dispersion is analyzed in detail through the study of the asymptotics at low and high frequencies, revealing new features ruling the wave propagation in continua where nonlocal characteristics must be taken into account. Global dispersive estimates and existence of conserved functionals are proved. A comparison between these new effects and the classical local scenario is deepened also through a numerical analysis.