Existence of Lower and Upper Solutions in Reverse Order with Respect to a Variable in a Model of Acidogenesis to Anaerobic Digestion

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.

References

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