Abstract
We study a nonlinear pseudodifferential equation describing the dynamics of dislocations in crystals. The long time asymptotics of solutions is described by the self-similar profiles.
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Biler, P., Karch, G. & Monneau, R. Nonlinear Diffusion of Dislocation Density and Self-Similar Solutions. Commun. Math. Phys. 294, 145–168 (2010). https://doi.org/10.1007/s00220-009-0855-8
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DOI: https://doi.org/10.1007/s00220-009-0855-8