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

Yuan Gao·Jian-Guo Liu
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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.

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Yuan Gao, Jian-Guo Liu. 2019-07-03. Long time behavior of dynamic solution to Peierls--Nabarro dislocation model. https://doi.org/10.4310/maa.2020.v27.n2.a4

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