Existence of solutions for a model describing the dynamics of junctions between dislocations

Nicolas Forcadel (1) , Régis Monneau (2)

1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

We study a dynamical version of a multi-phase field model of Koslowski and Ortiz for planar dislocation networks. We consider a two-dimensional vector field which describes phase transitions between constant phases. Each phase transition corresponds to a dislocation line, and the vectorial field description allows the formation of junctions between dislocations. This vector field is assumed to satisfy a non-local vectorial Hamilton-Jacobi equation with non-zero viscosity. For this model, we prove the existence for all time of a weak solution.

Mots clés: parabolic system of equations; Dislocation dynamics; non-local equations; junctions; parabolic system of equations.

Domaines: Equations aux dérivées partielles [math.AP]

Nicolas Forcadel, Régis Monneau. Existence of solutions for a model describing the dynamics of junctions between dislocations. SIAM Journal on Mathematical Analysis, 2009, 40 (6), pp. 2517-2535. ⟨10.1137/070710925⟩. ⟨hal-00197576⟩