Analysis of an atomistic model for anti-plane fracture
Analysis of PDEs
2019-11-07 v2
Abstract
We develop a model for an anti-plane crack defect posed on a square lattice under an interatomic pair-potential with nearest-neighbour interactions. In particular, we establish existence, local uniqueness and stability of solutions for small loading parameters and further prove qualitatively sharp far-field decay estimates. The latter requires establishing decay estimates for the corresponding lattice Green's function, which are of independent interest.
Keywords
Cite
@article{arxiv.1810.05501,
title = {Analysis of an atomistic model for anti-plane fracture},
author = {Maciej Buze and Thomas Hudson and Christoph Ortner},
journal= {arXiv preprint arXiv:1810.05501},
year = {2019}
}