Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Analysis of PDEs

arXiv:1410.4681 (math)
[Submitted on 17 Oct 2014 (v1), last revised 2 Jul 2015 (this version, v2)]

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

Authors:M. Crespo, B. Ivorra, A.M Ramos
View PDF
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.
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35K51
Cite as: arXiv:1410.4681 [math.AP]
  (or arXiv:1410.4681v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1410.4681

Submission history

From: Maria Crespo Moya [view email]
[v1] Fri, 17 Oct 2014 10:26:28 UTC (358 KB)
[v2] Thu, 2 Jul 2015 16:15:05 UTC (80 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.AP
< prev   |   next >
new | recent | 2014-10
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)