Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution

@article{Alvarez2006DislocationDS,
  title={Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution},
  author={Olivier Alvarez and Philippe Hoch and Yann Le Bouar and R{\'e}gis Monneau},
  journal={Archive for Rational Mechanics and Analysis},
  year={2006},
  volume={181},
  pages={449-504}
}
We study a mathematical model describing dislocation dynamics in crystals. We consider a single dislocation line moving in its slip plane. The normal velocity is given by the Peach-Koehler force created by the dislocation line itself. The mathematical model is an eikonal equation with a velocity which is a non-local quantity depending on the whole shape of the dislocation line. We study the special case where the dislocation line is assumed to be a graph or a closed loop. In the framework of… CONTINUE READING
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