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On a system of reaction–diffusion equations arising from competition with internal storage in an unstirred chemostat
- Source :
- Journal of Differential Equations. 248(10):2470-2496
- Publication Year :
- 2010
- Publisher :
- Elsevier BV, 2010.
-
Abstract
- In this paper we study a system of reaction–diffusion equations arising from competition of two microbial populations for a single-limited nutrient with internal storage in an unstirred chemostat. The conservation principle is used to reduce the dimension of the system by eliminating the equation for the nutrient. The reduced system (limiting system) generates a strongly monotone dynamical system in its feasible domain under a partial order. We construct suitable upper, lower solutions to establish the existence of positive steady-state solutions. Given the parameters of the reduced system, we answer the basic questions as to which species survives and which does not in the spatial environment and determine the global behaviors. The primary conclusion is that the survival of species depends on species's intrinsic biological characteristics, the external environment forces and the principal eigenvalues of some scalar partial differential equations. We also lift the dynamics of the limiting system to the full system.
- Subjects :
- Variable yield
Monotone dynamical system
Partial differential equation
Applied Mathematics
Scalar (physics)
Chemostat
Global stability
Dynamical system
Competition of algaes
Unstirred chemostat
Lower solutions
Droop's model
Domain (mathematical analysis)
Upper solutions
Internal storage
Maximum principle
Control theory
Reaction–diffusion system
Applied mathematics
Eigenvalues and eigenvectors
Analysis
Mathematics
Subjects
Details
- ISSN :
- 00220396
- Volume :
- 248
- Issue :
- 10
- Database :
- OpenAIRE
- Journal :
- Journal of Differential Equations
- Accession number :
- edsair.doi.dedup.....4755da01a74ee204489a15d0b1fa9799
- Full Text :
- https://doi.org/10.1016/j.jde.2009.12.014