Qualitative aspects in nonlocal dynamics

TL;DR

This paper explores the diverse dynamical behaviors of a linear one-dimensional nonlocal equation in peridynamics, analyzing propagation regimes and singularity formation through numerical studies.

Contribution

It provides a detailed numerical analysis of nonlocal dynamics, highlighting the transition from hyperbolic to dispersive regimes and singularity development.

Findings

Identification of different propagation regimes

Observation of singularity formation in initial value problems

Numerical characterization of nonlocal wave behaviors

Abstract

In this paper we investigate, through numerical studies, the dynamical evolutions encoded in a linear one-dimensional nonlocal equation arising in peridynamcs. The different propagation regimes ranging from the hyperbolic to the dispersive, induced by the nonlocal feature of the equation, are carefully analyzed. The study of an initial value Riemann-like problem suggests the formation of a singularity.