Nonlinear diffusion of dislocation density and self-similar solutions

Piotr Biler (1) , Grzegorz Karch (1) , Régis Monneau (2)

1 Instytut Matematyczny
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

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.

Mots clés: One-dimensional nonlinear pseudodifferential equation; viscosity solutions; self-similar solutions; stability

Domaines: Equations aux dérivées partielles [math.AP]

Piotr Biler, Grzegorz Karch, Régis Monneau. Nonlinear diffusion of dislocation density and self-similar solutions. Communications in Mathematical Physics, 2010, 294 (1), pp.145-168. ⟨10.1007/s00220-009-0855-8⟩. ⟨hal-00369429⟩