Generic properties of classical n-body systems, in one dimension, and crystal theory
Geometric structure of magnetic walls
After a short introduction on micromagnetism, we will focus on a scalar micromagnetic model. The problem, which is hyperbolic, can be viewed as a problem of Hamilton-Jacobi, and, similarly to conservation laws, it admits a kinetic formulation. We will use both points of view, together with tools from geometric measure theory, to prove the rectifiability of the singular set of micromagnetic configurations.
Ginzburg-Landau vortices : the static model
Global branching for discontinuous problems
Global existence and extinction of weak solutions to a class of semiconductor equations with fast diffusion terms.
Global existence for the discrete diffusive coagulation-fragmentation equations in L1.
Global solutions to vortex density equations arising from sup-conductivity
Global strong solutions of Vlasov's equation---necessary and sufficient conditions for their existence
Gravitational collapse of a Brownian gas
We investigate a model describing the dynamics of a gas of self-gravitating Brownian particles. This model can also have applications for the chemotaxis of bacterial populations. We focus here on the collapse phase obtained at sufficiently low temperature/energy and on the post-collapse regime following the singular time where the central density diverges. Several analytical results are illustrated by numerical simulations.
Ground state incongruence in 2D spin glasses revisited.