Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics
Analysis of PDEs
2022-10-26 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2105.01558,
title = {Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics},
author = {Giuseppe Maria Coclite and Serena Dipierro and Giuseppe Fanizza and Francesco Maddalena and Enrico Valdinoci},
journal= {arXiv preprint arXiv:2105.01558},
year = {2022}
}
Comments
40 pages, 12 figures