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Well posedness and stochastic derivation of a diffusion-growth-fragmentation equation in a chemostat

Abstract : We study the existence and uniqueness of the solution of a non-linear coupled system constituted of a degenerate diffusion-growth-fragmentation equation and a differential equation, resulting from the modeling of bacterial growth in a chemostat. This system is derived, in a large population approximation, from a stochastic individual-based model where each individual is characterized by a non-negative real valued trait described by a diffusion. Two uniqueness results are highlighted. They differ in their hypotheses related to the influence of the resource on individual trait dynamics, the main difficulty being the non-linearity due to this dependence and the degeneracy of the diffusion coefficient. Further we show that the semi-group of the stochastic trait dynamics admits a density by probabilistic arguments, that allows the measure solution of the diffusiongrowth-fragmentation equation to be a function with a certain Besov regularity.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03249697
Contributor : Josué Tchouanti Fotso <>
Submitted on : Friday, June 4, 2021 - 11:58:20 AM
Last modification on : Tuesday, July 20, 2021 - 5:16:01 PM

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  • HAL Id : hal-03249697, version 1

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Josué Tchouanti. Well posedness and stochastic derivation of a diffusion-growth-fragmentation equation in a chemostat. 2021. ⟨hal-03249697⟩

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