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Asymptotic stability of a coupled Advection-Diffusion-Reaction system arising in bioreactor processes.

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Crespo Moya, María and Ramos del Olmo, Ángel Manuel and Ivorra, Benjamin (2016) Asymptotic stability of a coupled Advection-Diffusion-Reaction system arising in bioreactor processes. (Unpublished)

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Abstract

In this work, we perform an asymptotic analysis of a coupled system of two Advection-Diffusion-Reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacterias), called biomass, and a diluted organic contaminant (e.g., nitrates), called substrate, in a continuous flow bioreactor. This system exhibits, under suitable conditions, two stable equilibrium states: one steady state in which the biomass becomes extinct and no reaction is produced, called washout, and another steady state, which corresponds to the partial elimination of the substrate. We use the method of linearization to give sufficient conditions for the asymptotic stability of the two stable equilibrium configurations. Finally, we compare our asymptotic analysis with the usual asymptotic analysis associated to the continuous bioreactor when it is modeled with ordinary differential equations.


Item Type:Article
Uncontrolled Keywords:Asymptotic stability; bioprocesses; Advection-Diffusion-Reaction; separation of variables
Subjects:Sciences > Mathematics > Mathematical analysis
Sciences > Mathematics > Numerical analysis
ID Code:39501
Deposited On:21 Oct 2016 11:28
Last Modified:12 Dec 2018 15:06

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