This article is cited in 1 paper

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. Higuera^ab, A. V. Sinitsyn<sup>c

a</sup> 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.

UDC: 620.95+517.927

MSC: 34A40

Received: 11.03.2015

Language: English

DOI: 10.14529/mmp150205

Bibliographic databases:

• 
•