Geodesic
On properties of solutions to one system modeling a multistage substance synthesis
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 3, pp. 86-94 
I. I. Matveeva; A. M. Popov. On properties of solutions to one system modeling a multistage substance synthesis. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 3, pp. 86-94. http://geodesic.mathdoc.fr/item/VNGU_2009_9_3_a5/
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     title = {On properties of solutions to one system modeling a multistage substance synthesis},
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     url = {http://geodesic.mathdoc.fr/item/VNGU_2009_9_3_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Cauchy problem for a system of ordinary differential equations modeling a multistage substance synthesis is considered. We study properties of the last component of its solution, describing the concentration of the synthesis product, as a function of the parameter $\tau$ characterizing the total time of the synthesis process. The continuous dependence on $\tau$ is established, estimates for the continuity module are obtained. We prove the uniform convergence as $\tau \to 0$; moreover, the limit function is a solution to the Cauchy problem for one ordinary differential equation.

[1] Likhoshvai V. A., Fadeev S. I., Demidenko G. V. i dr., “Modelirovanie uravneniem s zapazdyvayuschim argumentom mnogostadiinogo sinteza bez vetvleniya”, Sib. zhurn. industr. matematiki, 7:1 (2004), 73–94 | MR

[2] Demidenko G. V., Kolchanov N. A., Likhoshvai V. A. i dr., “Matematicheskoe modelirovanie regulyatornykh konturov gennykh setei”, Zhurn. vych. mat. i mat. fiziki, 44:12 (2004), 2276–2295 | MR | Zbl

[3] Golubyatnikov V. P., Demidenko G. V., Evdokimov A. A. i dr., “Teoriya gennykh setei”, Sistemnaya kompyuternaya biologiya, eds. N. A. Kolchanov, S. S. Goncharov, V. A. Likhoshvai, V. A. Ivanisenko, Izd-vo SO RAN, Novosibirsk, 2008, 397–480

[4] Matveeva I. I., Popov A. M., “Matrix Process Modelling: Dependence of Solutions of a System of Differential Equations on Parameter”, Proc. of the Fifth Int. Conf. Bioinformatics of Genome Regulation and Structure (Novosibirsk, Russia, July 16–22, 2006), v. 3, Institute of Cytology and Genetics, Novosibirsk, 2006, 82–85

[5] Godunov S. K., Obyknovennye differentsialnye uravneniya s postoyannymi koeffitsientami, Novosibirsk, 1994