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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. 357377. ISSN 15787303

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Official URL: http://link.springer.com/article/10.1007%2Fs1339801502373
URL  URL Type 

http://arxiv.org/abs/1410.4681  Organisation 
http://www.springer.com  Publisher 
Abstract
In this work, we study the mathematical analysis of a coupled system of two reactiondiffusionadvection 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; Reactiondiffusionadvection; 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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