Single species growth consuming inorganic carbon with internal storage in a poorly mixed habitat
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This paper presents a PDE system modeling the growth of a single species population consuming inorganic carbon that is stored internally in a poorly mixed habitat. Inorganic carbon takes the forms of “CO2” (dissolved CO2 and carbonic acid) and “CARB” (bicarbonate and carbonate ions), which are substitutable in their effects on algal growth. We first establish a threshold type result on the extinction/persistence of the species in terms of the sign of a principal eigenvalue associated with a nonlinear eigenvalue problem. If the habitat is the unstirred chemostat, we add biologically relevant assumptions on the uptake functions and prove the uniqueness and global attractivity of the positive steady state when the species persists.
KeywordsInorganic carbon Internal storage Extinction Persistence Global stability A nonlinear eigenvalue problem
Mathematics Subject Classification35B40 35K57 92D25
We are grateful to three anonymous referees for their careful reading and helpful suggestions which led to improvements of our original manuscript. We also express our thanks to Prof. H. R. Thieme for suggesting us the key reference Mallet-Paret and Nussbaum (2010) in this paper.
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