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

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.

25 pages

Cited by in corpus (2)

• Existence and uniqueness of bounded stable solutions to the Peierls-Nabarro model for curved dislocations
• Existence and rigidity of the Peierls-Nabarro model for dislocations in high dimensions