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April  2020, 19(4): 2333-2346. doi: 10.3934/cpaa.2020101

## Analysis of an anaerobic digestion model in landfill with mortality term

 1 Interdisciplinary Laboratory for Natural Resources and Environment, Ibn Tofaïl University, Kénitra, Morocco 2 IRIMAS, University of Haute-Alsace, Mulhouse, France, University of Strasbourg, France 3 LBE, University of Montpellier, INRA, Narbonne, France 4 MISTEA, University of Montpellier, INRA, Montpellier SupAgro, Montpellier, France 5 University of Haute-Alsace, IRIMAS UR 7499, F-68100 Mulhouse, France, University of Strasbourg, France

*Corresponding author

Dedicated to Professor Tomás Caraballo on the occasion of his 60-th birthday

Received  August 2019 Revised  October 2019 Published  January 2020

We study a mathematical model of anaerobic digestion with biomass recirculation, dedicated to landfill problems, and analyze its asymptotic behavior. We show that the global attractor is composed of an infinity of non-hyperbolic equilibria. For non-monotonic growth functions, this set is non connected, which impacts the performances of the bioprocess.

Citation: S. Ouchtout, Z. Mghazli, J. Harmand, A. Rapaport, Z. Belhachmi. Analysis of an anaerobic digestion model in landfill with mortality term. Communications on Pure & Applied Analysis, 2020, 19 (4) : 2333-2346. doi: 10.3934/cpaa.2020101
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##### References:
Overall scheme of the anaerobic degradation of organic matter
Graphs of Monod and Haldane functions
Graph of the Haldane function considered in the example
Graph of $S(\cdot)$ for initial conditions $X_0 = 340$ to $X_0 = 360$ with a step of 5
Threshold on $X_0$ as a function of $K_d$ for model parameters indicated in Table 1
Biogas production as a function of $X_0$ for $K_d = 0.02$
$\lambda^-$, $\lambda^+$ (on top) ${\rm Biogas}^-$ and ${\rm Biogas}^+$ (on bottom) as functions of $K_d$
 $K_h$ $Y$ $f_1$ $f_2$ $\alpha$ 0.176 0.05 0.7 0.76 0.9
 $K_h$ $Y$ $f_1$ $f_2$ $\alpha$ 0.176 0.05 0.7 0.76 0.9
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