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Existence and Uniqueness of Solution of a Continuous Flow Bioreactor Model with Two Species.

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Crespo Moya, María and Ivorra, Benjamin and Ramos del Olmo, Ángel Manuel (2016) Existence and Uniqueness of Solution of a Continuous Flow Bioreactor Model with Two Species. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 110 (2). pp. 357-377. ISSN 1578-7303

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Official URL: http://link.springer.com/article/10.1007%2Fs13398-015-0237-3




Abstract

In this work, we study the mathematical analysis of a coupled system of two reaction-diffusion-advection equations and Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacterias) and a diluted substrate (e.g., nitrate) in a continuous flow bioreactor. This type of bioreactor can be used, for instance, for water treatment. First, we prove the existence and uniqueness of solution, under the hypothesis of linear reaction by using classical results for linear parabolic boundary value problems. Next, we prove the existence and uniqueness of solution for some nonlinear reactions by applying \textit{Schauder Fixed Point Theorem} and the theorem obtained for the linear case. Results about the nonnegativeness and boundedness of the solution are also proved here.


Item Type:Article
Uncontrolled Keywords:Existence; Uniqueness; Reaction-diffusion-advection; Nonlinear parabolic system; Bioreactor
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
Sciences > Mathematics > Differential equations
ID Code:27106
Deposited On:03 Nov 2014 07:31
Last Modified:12 Dec 2018 15:06

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