Séance Séminaire

Séminaire ACSIOM

Analysis of systems with small cross-diffusion

I will present recent results concerning a class of nonlinear parabolic systems of partial differential equations with small cross-diffusion. Such systems have been proposed to describe the macroscopic dynamics of a variety of large systems of interacting agents of different species and they can be interpreted as (nonlinear) perturbations of a simpler PDE model. I will discuss well-posedness, regularity, stability and convergence to the stationary state for solutions in an appropriate Banach space. I will also present some applications and refinements of the above-mentioned results for specific models.