Asymptotic stability of a coupled advection-diffusion-reaction system arising in bioreactor processes

Date

2017-08-07

Authors

Crespo, Maria
Ivorra, Benjamin
Ramos, Angel M.

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Publisher

Texas State University, Department of Mathematics

Abstract

In this work, we present 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., bacteria), 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 linearization method to give sufficient conditions for the linear 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.

Description

Keywords

Asymptotic stability, Advection-diffusion-reaction system, Dimensional analysis, Continuous bioreactor

Citation

Crespo, M., Ivorra, B., & Ramos, A. M. (2017). Asymptotic stability of a coupled advection-diffusion-reaction system arising in bioreactor processes. <i>Electronic Journal of Differential Equations, 2017</i>(194), pp. 1-26.

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Attribution 4.0 International

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