This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Patrizi, StefaniaValdinoci, Enrico2016-12-152019-06-2820162198-5855https://doi.org/10.34657/2632https://oa.tib.eu/renate/handle/123456789/3146We describe the asymptotic states for the solutions of a nonlocal equation of evolutionary type, which have the physical meaning of the atom dislocation function in a periodic crystal. More precisely, we can describe accurately the smoothing effect on the dislocation function occurring slightly after a particle collision (roughly speaking, two opposite transitions layers average out) and, in this way, we can trap the atom dislocation function between a superposition of transition layers which, as time flows, approaches either a constant function or a single heteroclinic (depending on the algebraic properties of the orientations of the initial transition layers). The results are endowed of explicit and quantitative estimates and, as a byproduct, we show that the ODE systems of particles that governs the evolution of the transition layers does not admit stationary solutions (i.e., roughly speaking, transition layers always move).application/pdfeng510Peierls-Nabarro modelnonlocal integro-differential equationsdislocation dynamicsattractive/repulsive potentialscollisionsReport