Abstract
A system of reaction-diffusion equations arising from the unstirred chemostat model with ratio-dependent function is considered. The asymptotic behavior of solutions is given and all positive steady-state solutions to this model lie on a single smooth solution curve. It turns out that the ratio-dependence effect will not affect the dynamics, compared with (Hsu and Waltman in SIAM J. Appl. Math. 53(4):1026–1044, 1993) and (Nie and Wu in Sci. China Math. 56(10):2035–2050, 2013).
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The authors gratefully acknowledge the referee for his/her comments and suggestions, which have significantly improved not only the presentation but the overall quality of the paper.
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The work has been partially supported by the Natural Science Foundation of China (Grant Nos.: 11771262, 61872227), and the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2018JQ1021).
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Yang, W. Existence and Asymptotic Behavior of Solutions for the Unstirred Chemostat Model with Ratio-Dependent Function. Acta Appl Math 166, 223–232 (2020). https://doi.org/10.1007/s10440-019-00264-2
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DOI: https://doi.org/10.1007/s10440-019-00264-2