In this paper, we study a non-local coupled system that arises in the theory of dislocations densities dynamics. Within the framework of viscosity solutions, we prove a long time existence andâ€¦ (More)

In this paper we prove the convergence at a large scale of a non-local first order equation to an anisotropic mean curvature motion. This is an eikonal-type equation with a velocity depending in aâ€¦ (More)

This paper is concerned with the homogenization of a non-local first order Hamilton-Jacobi equation describing the dynamics of several dislocation lines and the homogenization of some particleâ€¦ (More)

In this article, we study the existence and the uniqueness of traveling waves for a discrete reaction-diffusion equation with bistable non-linearity, namely a generalization of the fully overdampedâ€¦ (More)

We consider systems of ODEs that describe the dynamics of particles. Each particle satisfies a Newton law (including a damping term and an acceleration term) where the force is created by theâ€¦ (More)

In this article, we present briefly the mathematical study of the dynamics of line defects called dislocations, in crystals. The mathematical model is an eikonal equation describing the motion of theâ€¦ (More)

This paper is concerned with the homogenization of some particle systems with two-body interactions in dimension one and of dislocation dynamics in higher dimensions. The dynamics of our particleâ€¦ (More)

In this paper, we study the motion of spirals by mean curvature type motion in the (two dimensional) plane. Our motivation comes from dislocation dynamics; in this context, spirals appear when aâ€¦ (More)

In this paper, we study the existence and uniqueness of traveling wave solution for the accelerated Frenkel-Kontorova model. This model consists in a system of ODE that describes the motion particlesâ€¦ (More)

In this paper, we study the motion of spirals by mean curvature in a (two dimensional) plane. Our motivation comes from dislocation dynamics; in this context, spirals appear when a screw dislocationâ€¦ (More)