A system of resource-based growth models with two resources in the unstirred chemostat
type: Item
instance of: scholarly article
title: A system of resource-based growth models with two resources in the unstirred chemostat
zbMATH Open document ID: 1001.80007
author: Jianhua Wu
author: Gail S. K. Wolkowicz
published in: Journal of Differential Equations
publication date: 2002-07-09T00:00:00Z
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 80A32
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 37G35
Mathematics Subject Classification ID: 37N25
zbMATH DE Number: 1642567
zbMATH Keywords: systems of reaction-diffusion equation
zbMATH Keywords: maximum principle
zbMATH Keywords: nonlinear eigenvalues
zbMATH Keywords: unstirred chemostat
zbMATH Keywords: nutrient concentrations
zbMATH Keywords: dilution rate
zbMATH Keywords: positive steady-state solution
MaRDI profile type: Publication
full work available at URL: jdeq.2000.3870
OpenAlex ID: W1970299973
cites work: Exploitative Competition of Microorganisms for Two Complementary Nutrients in Continuous Cultures
cites work: Q3885576
cites work: An examination of the thresholds of enrichment: A resource-based growth model
cites work: Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources
cites work: Exploitative competition in the chemostat for two perfectly substitutable resources
cites work: A nonlinear boundary value problem arising from competition in the chemostat
cites work: The Theory of the Chemostat
cites work: On a System of Reaction-Diffusion Equations Arising from Competition in an Unstirred Chemostat
cites work: Q4844548
cites work: Q4321824
cites work: Nonlinear boundary value problems and competition in the chemostat
cites work: A parabolic system modeling microbial competition in an unmixed bio-reactor
cites work: Q4247769
cites work: Global bifurcation of coexistence state for the competition model in the chemostat
cites work: Q5666915
cites work: Q4746129
cites work: Q4023219
cites work: Bifurcation from simple eigenvalues
cites work: Some global results for nonlinear eigenvalue problems
cites work: Q4872220
cites work: Persistence in Infinite-Dimensional Systems
DOI: 10.1006/JDEQ.2000.3870
review text: This paper is devoted to the two extreme cases in the unstirred chemostat. Let \(S(t)\), \(R(t)\) denote the nutrient concentrations at time \(t\) and \(u(t)\) is the biomass of the population in the culture vessel, then the well-stirred complementary model is given by NEWLINE\[NEWLINE\begin{aligned} S_t & = (S^0-S) D-{1\over y_s} h(S,R)u\\ R_t & =(R^0-R) D-{1\over y_R}h(S,R)u \tag{1}\\ u_t & =[-D+h(S,R)] u\end{aligned}NEWLINE\]NEWLINE where \(S^0>0\) and \(R^0>0\) are constants that represent the input concentrations of the nutrients \(S\) and \(R\), respectively, and \(D\) is the dilution rate, \(y_s\) and \(y_R\) are the corresponding growth yields constants; \(h(S,R)\) is called the response function. The authors establish the existence and uniqueness of a positive steady-state solution for (1). It is also proved that the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values.
description: scientific article; zbMATH DE number 1642567