Existence of lower and upper solutions in reverse order with respect to a variable in a model of acidogenesis to anaerobic digestion
Автор: Higuera M.M., Sinitsyn A.V.
Рубрика: Математическое моделирование
Статья в выпуске: 2 т.8, 2015 года.
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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.
Upper-lower solutions, inverse order, system of nonlinear differential equations, anaerobic digestion
Короткий адрес: https://sciup.org/147159319
IDR: 147159319 | DOI: 10.14529/mmp150205
Список литературы Existence of lower and upper solutions in reverse order with respect to a variable in a model of acidogenesis to anaerobic digestion
- Jewell W. Anaerobic Sewage Treatment. Environmental Science and Technology, 1987, vol. 21, no. 1, pp. 9-21. DOI: DOI: 10.1021/es00155a002
- Bernard O., Sadok Z.H., Dochain D., Genovesi A., Steyer J. -P. Dynamical Model Development and Parameter Identification for an Anaerobic Wastewater Treatment Process. Biotechnology and Bioengineering, 2001, vol. 75, no. 4, pp. 424-438. DOI: DOI: 10.1002/bit.10036
- Alcaraz V., Genovesi A., Harmand J., González V., Rapaport A., Steyer J.P. Robust Exponetial Nonlinear Interval Observers for a Class of Lumped Models Useful in Chemical and Biochemical Engineering. Application to a Wastewater Treatment Process. International Workshop on Application of Interval Analysis to Systems and Control, MISC'99, Girona, Spain, 1999, pp. 24-26.
- Pao C.-V. Nonlinear Parabolic and Elliptic Equations. N.Y., Plenum Press, 1992.
- Delgado M., Suarez A. Existence of Solutions for Elliptic Systems with Hölder Continuous Nonlinearities. Diferential and Integral Equations, 2000, vol. 13, no. 4, 6, pp. 453-477.
- Franco D., Nieto J.J., O'Regan D. Upper and Lower Solutions for First Order Problems with Nonlinear Boundary Conditions. Estracta Mathematicae, 2003, vol. 18, no. 2, pp. 153-160
- Benyahia B., Sari T., Cherki B., Harmand J. Bifurcation and Stability Analysis of a Two Step Model for Monitoring Anaerobic Digestion Processes. Journal of Process Control, 2012, vol. 22, no. 6, pp. 1008-1019. DOI: DOI: 10.1016/j.jprocont.2012.04.012
- Sidorov N., Loginov B., Sinitsyn A., Falaleev M. Lyapunov -Schmidt Methods in Nonlinear Analysis and Applications. Dordrecht, Boston, London, Kluwer Academic Publisher, 2002. 568 p. DOI: DOI: 10.1007/978-94-017-2122-6
- Sviridyuk G.A., Fedorov V.E. Linear Sobolev Type Equations and Degenerate Semigroups of Operators. Utrecht, Boston, Koln, Tokyo, VSP, 2003. 216 p. DOI: DOI: 10.1515/9783110915501
- Lorenzo Y., Obaya M.C. La digestion anaerobia. Aspectos teoricos. Parte I. ICIDCA. Sobre los Derivados de la Cana de Azucar, 2005, vol. 39, no. 1, pp. 35-48.
- McKenna P.-J., Walter W. On the Dirichlet Problem for Elliptic Systems. Applicable Analysis, 1986, no. 21, pp. 207-224. DOI: DOI: 10.1080/00036818608839592
- Salinas E., Munoz R., Sosa J.-C., Lopez B. Analysis to the Solutions of Abel's Differential Equations of the First Kind under Transformation y=u(x)z(x)+v(x). Applied Mathematical Sciences, 2013, vol. 7, no. 42, pp. 2075-2092.
