Long-time asymptotics for evolutionary crystal dislocation models

DOI10.1016/j.aim.2020.107242zbMath1446.35198arXiv1907.01491OpenAlexW2954708106MaRDI QIDQ776807

Juan Dávila, Matteo Cozzi, Manuel A. del Pino

Publication date: 13 July 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.01491

zbMATH Keywords

long-time asymptoticsfractional Laplaciannonlocal parabolic equationPeierls-Nabarro model

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Dynamical systems in solid mechanics (37N15) Fractional derivatives and integrals (26A33) Long-time behavior of solutions for dynamical problems in solid mechanics (74H40) Crystals in solids (74N05) PDEs in connection with mechanics of deformable solids (35Q74) Initial value problems for PDEs with pseudodifferential operators (35S10) Semilinear parabolic equations (35K58) Fractional partial differential equations (35R11)

Related Items (6)

A fractional glance to the theory of edge dislocations ⋮ Derivation of the 1-D Groma-Balogh equations from the Peierls-Nabarro model ⋮ The stickiness property for antisymmetric nonlocal minimal graphs ⋮ Solutions with single radial interface of the generalized Cahn-Hilliard flow ⋮ From the Peierls-Nabarro model to the equation of motion of the dislocation continuum ⋮ On the Harnack inequality for antisymmetric \(s\)-harmonic functions

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