Maria Crespo, Benjamin Ivorra, Angel Manuel Ramos
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.
Submitted March 1, 2017. Published August 7, 2017.
Math Subject Classifications: 35B30, 35B35, 35B40, 35K51, 35Q35.
Key Words: March 1, 2017. Published August 8, 2017.
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María Crespo UMR MISTEA - Mathématiques, Informatique et Statistique pour lÉnvironnement et lÁgronomie (INRA/SupAgro). 2, Place P.Viala 34060 Montpellier, France email: maria.crespo-moya@umontpellier.fr | |
Benjamin Ivorra Departamento de Matemáatica Aplicada & Instituto de Matemáatica Interisciplinar Universidad Complutense de Madrid Plaza de Ciencias, 3, 28040 Madrid, Spain email: ivorra@ucm.es | |
áAngel Manuel Ramos Departamento de Matemáatica Aplicada & Instituto de Matemáatica Interisciplinar Universidad Complutense de Madrid Plaza de Ciencias, 3, 28040 Madrid, Spain email: angel@mat.ucm.es |
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