Solutions périodiques de systèmes hamiltoniens
Travelling fronts in cylinders
On singular perturbation problems with Robin boundary condition
We consider the following singularly perturbed elliptic problem where satisfies some growth conditions, , and () is a smooth and bounded domain. The cases (Neumann problem) and (Dirichlet problem) have been studied by many authors in recent years. We show that, there exists a generic constant such that, as , the least energy solution has a spike near the boundary if , and has an interior spike near the innermost part of the domain if . Central to our study...
Non-planar fronts in Boussinesq reactive flows
Further qualitative properties for elliptic equations in unbounded domains
A numerical study of some questions in vortex rings theory
Speed-up of reaction-diffusion fronts by a line of fast diffusion
In these notes, we discuss a new model, proposed by H. Berestycki, J.-M. Roquejoffre and L. Rossi, to describe biological invasions in the plane when a strong diffusion takes place on a line. This model seems relevant to account for the effects of roads on the spreading of invasive species. In what follows, the diffusion on the line will either be modelled by the Laplacian operator, or the fractional Laplacian of order less than 1. Of interest to us is the asymptotic speed of spreading in the direction...
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