A numerical study for the homogeneization of one-dimensional models describing the motion of dislocations, accepted to Int

In this paper we are interested in the collective motion of dislocations defects in crystals. Mathematically we study the homogenization of a non-local Hamilton-Jacobi equation. We prove some qualitative properties on the eective hamiltonian. We also provide a numerical scheme which is proved to be monotone under some suitable CFL conditions. Using this scheme, we compute numerically the eective hamiltonian. Furthermore we also provide numerical computations of the eective hamiltonian for several models corresponding to the dynamics of dislocations where no theoretical analysis is available