Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics

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.

Automated summary

This study analyzes the interplay between nonlocality and dispersion in a linear equation inspired by peridynamics models. Global dispersive estimates and the existence of conserved functionals are proven through the study of low and high frequency asymptotics. A comparison with the classical local scenario is deepened through numerical analysis.