Further studies of a reaction-diffusion system for an unstirred chemostat with internal storage

Sze-Bi Hsu; Junping Shi; Feng-Bin Wang

doi:10.3934/dcdsb.2014.19.3169

Article Contents

2014, Volume 19, Issue 10: 3169-3189. Doi: 10.3934/dcdsb.2014.19.3169

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Further studies of a reaction-diffusion system for an unstirred chemostat with internal storage

1.
Department of Mathematics and The National Center for Theoretical Science, National Tsing-Hua University, Hsinchu 30013
2.
Department of Mathematics, College of William and Mary, Williamsburg, Virginia, 23187-8795
3.
Department of Natural Science in the Center for General Education, Chang Gung University, Kwei-Shan, Taoyuan 333

Received: June 2013

Revised: August 2013

Published: December 2014

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Abstract

The dynamics of a reaction-diffusion system for two species of microorganism in an unstirred chemostat with internal storage is studied. It is shown that the diffusion coefficient is a key parameter of determining the asymptotic dynamics, and there exists a threshold diffusion coefficient above which both species become extinct. On the other hand, for diffusion coefficient below the threshold, either one species or both species persist, and in the asymptotic limit, a steady state showing competition exclusion or coexistence is reached.

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Mathematics Subject Classification: 35K51, 35K57, 35B35, 92D25.

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