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Long time behavior of dynamic solution to Peierls--Nabarro dislocation model (1907.02002v1)
Published 3 Jul 2019 in math.AP and nlin.PS
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.