Convergence towards equilibrium for a model with partial diffusion - Analytical Genomics Access content directly
Preprints, Working Papers, ... (Preprint) Year : 2022

Convergence towards equilibrium for a model with partial diffusion

Delphine Salort
Didier Smets

Abstract

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.
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Dates and versions

hal-03845918 , version 1 (09-11-2022)

Identifiers

  • HAL Id : hal-03845918 , version 1

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