Mark Peletier

Technische Universiteit Eindhoven

Continuum limit for annihilating dislocations in one dimension

We prove a many-particle limit for the evolution of a system of particles in one dimension with positive and negative charges. The particles interact via a logarithmic potential, and when particles of opposite sign meet they ‘annihilate’ and are removed from the system.

We use the framework of viscosity solutions for this system developed by Forcadel, Imbert, and Monneau (2009), which in turn is based on Slepcev’s formulation (2003) of non-local level-set evolutions. We generalize their convergence proof to the case of singular interactions and multiple signs by a careful analysis of both the ODE system and the Hamiltonian near annihilation points.

This is joint work with Patrick van Meurs and Norbert Pozar (both Kanazawa University, Japan)