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.
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