Scaling limits for a population model with growth, division and cross-diffusion - Archive ouverte HAL
Preprints, Working Papers, ... Year : 2024

Scaling limits for a population model with growth, division and cross-diffusion

Abstract

Originally motivated by the morphogenesis of bacterial microcolonies, the aim of this article is to explore models through different scales for a spatial population of interacting, growing and dividing particles. We start from a microscopic stochastic model, write the corresponding stochastic differential equation satisfied by the empirical measure, and rigorously derive its mesoscopic (mean-field) limit. Under smoothness and symmetry assumptions for the interaction kernel, we then obtain entropy estimates, which provide us with a localization limit at the macroscopic level. Finally, we perform a thorough numerical study in order to compare the three modeling scales.
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Dates and versions

hal-04740457 , version 1 (16-10-2024)

Identifiers

  • HAL Id : hal-04740457 , version 1

Cite

Marie Doumic, Sophie Hecht, Marc Hoffmann, Diane Peurichard. Scaling limits for a population model with growth, division and cross-diffusion. 2024. ⟨hal-04740457⟩
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