Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics

TL;DR

This paper investigates how nonlocal interactions influence wave dispersion in a one-dimensional scalar wave model inspired by peridynamics, revealing new wave propagation features and providing theoretical and numerical insights.

Contribution

It introduces a detailed analysis of dispersive effects in a nonlocal wave equation, including asymptotic behavior, estimates, conserved quantities, and comparison with classical models.

Findings

Identification of new dispersive features due to nonlocality

Global dispersive estimates established for the model

Numerical analysis comparing nonlocal and local wave behaviors

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 {\it scenario} is deepened also through a numerical analysis.