Nonlinear Diffusion of Dislocation Density and Self-Similar Solutions

Communications in Mathematical Physics volume 294, Article number: 145 (2010) Cite this article

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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Affiliations

  1. Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland

    Piotr Biler & Grzegorz Karch

  2. CERMICS, École Nationale des Ponts et Chaussées, 6 et 8 Avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455, Marne-la-Vallée Cedex 2, France

    Régis Monneau

Authors
  1. Piotr Biler
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  2. Grzegorz Karch
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  3. Régis Monneau
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Correspondence to Piotr Biler.

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Communicated by P. Constantin

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Biler, P., Karch, G. & Monneau, R. Nonlinear Diffusion of Dislocation Density and Self-Similar Solutions. Commun. Math. Phys. 294, 145 (2010). https://doi.org/10.1007/s00220-009-0855-8

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Keywords

  • Dislocation Density
  • Viscosity Solution
  • Comparison Principle
  • Decay Estimate
  • Nonlinear Diffusion