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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2015, Volume 8, Issue 2, Pages 55–68 (Mi vyuru263)  

Mathematical Modelling

Existence of lower and upper solutions in reverse order with respect to a variable in a model of acidogenesis to anaerobic digestion

M. M. Higueraab, A. V. Sinitsync

a Faculty of Natural Sciences and Mathematics, Research Group Naturatu, University of Ibague, Ibague-Tolima, Colombia
b Faculty of Mathematics, University of Veracruz, Mexico
c Department of Mathematics, National University of Colombia, Bogota, Colombia

Abstract: We prove existence of upper and lower solutions in reverse order with respect a part of the variables in a system of nonlinear ordinary differential equations modelling acidogenesis in anaerobic digestion. The corresponding existence theorems are established. The upper and lower solutions are constructed analytically, by defining semi-trivial solutions for each of the variables in the model. We introduce the concept of indicator semi-trivial solutions. Finally, we numerically solve the system supported by the Matlab software and matching the graphs of the numerical solutions with analytical solutions is found.

Keywords: upper-lower solutions; inverse order; system of nonlinear differential equations; anaerobic digestion.

DOI: https://doi.org/10.14529/mmp150205

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Bibliographic databases:

UDC: 620.95+517.927
MSC: 34A40
Received: 11.03.2015
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Citation: M. M. Higuera, A. V. Sinitsyn, “Existence of lower and upper solutions in reverse order with respect to a variable in a model of acidogenesis to anaerobic digestion”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:2 (2015), 55–68

Citation in format AMSBIB
\Bibitem{HigSin15}
\by M.~M.~Higuera, A.~V.~Sinitsyn
\paper Existence of lower and upper solutions in reverse order with respect to a variable in a model of acidogenesis to anaerobic digestion
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2015
\vol 8
\issue 2
\pages 55--68
\mathnet{http://mi.mathnet.ru/vyuru263}
\crossref{https://doi.org/10.14529/mmp150205}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000422200600005}
\elib{http://elibrary.ru/item.asp?id=23442153}


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