English

Long time behavior of dynamic solution to Peierls--Nabarro dislocation model

Analysis of PDEs 2022-11-08 v1 Pattern Formation and Solitons

Abstract

In this paper we study the relaxation process of Peierls-Nabarro dislocation model, which is a gradient flow with singular nonlocal energy and double well potential describing how the materials relax to its equilibrium with the presence of a dislocation. We prove the dynamic solution to Peierls-Nabarro model will converge exponentially to a shifted steady profile which is uniquely determined.

Keywords

Cite

@article{arxiv.1907.02002,
  title  = {Long time behavior of dynamic solution to Peierls--Nabarro dislocation model},
  author = {Yuan Gao and Jian-Guo Liu},
  journal= {arXiv preprint arXiv:1907.02002},
  year   = {2022}
}

Comments

25 pages

R2 v1 2026-06-23T10:11:25.053Z