Convergence towards equilibrium for a model with partial diffusion

Delphine Salort (1) , Didier Smets (2)

1 LCQB-AG - Analytical Genomics [LCQB]
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We study the asymptotic behavior of a two dimensional linear PDE with a degenerate diffusion and a drift term. The structure of this equation typically arises in some mathematical mean fields models of neural network, and the investigation of the qualitative properties of this equation is still open, and a challenging question. We prove, via a Doeblin-Harris type method, that the solutions converge exponentially fast to the unique stationary state in a L 1-weighted norm.

Domaines: Mathématiques [math]

Delphine Salort, Didier Smets. Convergence towards equilibrium for a model with partial diffusion. 2022. ⟨hal-03845918⟩