Analysis of an atomistic model for anti-plane fracture. (arXiv:1810.05501v1 [math.AP])

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. 查看全文>>