Geodesic
Existence of lower and upper solutions in reverse order with respect to a variable in a model of acidogenesis to anaerobic digestion
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 2, pp. 55-68

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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. 
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     author = {M. M. Higuera and A. V. Sinitsyn},
     title = {Existence of lower and upper solutions in reverse order with respect to a variable in a model of acidogenesis to anaerobic digestion},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {55--68},
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     number = {2},
     year = {2015},
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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 Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 2, pp. 55-68. http://geodesic.mathdoc.fr/item/VYURU_2015_8_2_a4/