English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the existence and uniqueness of the solution of a non-linear coupledsystem constituted of a degenerate diffusion-growth-fragmentation equation anda differential equation, resulting from the modeling of bacterial growth in achemostat. This system is derived, in a large population approximation, from astochastic individual-based model where each individual is characterized by anon-negative real valued trait described by a diffusion. Two uniqueness resultsare highlighted. They differ in their hypotheses related to the influence ofthe resource on individual trait dynamics, the main difficulty being thenon-linearity due to this dependence and the degeneracy of the diffusioncoefficient. Further we show that the semi-group of the stochastic traitdynamics admits a density by probabilistic arguments, that allows the measuresolution of the diffusiongrowth-fragmentation equation to be a function with acertain Besov regularity.

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