Binary correspondences and the inverse problem of chemical kinetics
Автор: Gutman Alexander E., Kononenko Larasa I.
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 3 т.20, 2018 года.
Бесплатный доступ
We show how binary correspondences can be used for simple formalization of the notion of problem, definition of the basic components of problems, their properties, and constructions. In particular, formalization of the following notions is presented: condition, data, unknowns, and solutions of a problem, solvability and unique solvability, inverse problem, composition and restriction of problems, isomorphism between problems. We also consider topological problems and the related notions of stability and correctness. A connection is indicated between the stability and continuity of a uniquely solvable topological problem. The definition of parametrized set is given. The notions are introduced of parametrized problem, the problem of reconstruction of an object by the values of parameters, as well as the notions of locally free set of parameters and stability with respect to a set of parameters. As an illustration, we consider a singularly perturbed system of ordinary differential equations which describe a process in chemical kinetics and burning...
Binary correspondence, inverse problem, solvability, composition, stability, correctness, differential equation, chemical kinetics, linear independence
Короткий адрес: https://sciup.org/143168770
IDR: 143168770 | DOI: 10.23671/VNC.2018.3.17981
Список литературы Binary correspondences and the inverse problem of chemical kinetics
- Gutman A. E., Kononenko L. I. Formalization of Inverse Problems and its Applications, Sibirskij zhurnal chistoj i prikladnoj matematiki , 2017, vol. 17, no. 4, pp. 49-56 DOI: 10.17377/PAM.2017.17.5
- Gutman A. E., Kononenko L. I. The Inverse Problem of Chemical Kinetics as a Composition of Binary Correspondences. Sibirskie elektronnye matematicheskie izvestiya , 2018, vol. 15, pp. 48-53. semi.2018.15.006 DOI: 10.17377/\allowbreak
- Gutman A. E., Koptev A. V. Finite Dimensionality and Separability of the Stalks of Banach Bundles, Siberian Mathematical Journal, 2014, vol. 55, no. 2, pp. 246-253 DOI: 10.1134/s0037446614020074
- Kononenko L. I. Qualitative Analysis of Singularly Perturbed Systems with One or Two Slow and Fast Variables, Sibirskij zhurnal industrialnoj matematiki , 2002, vol. 5, no. 4, pp. 55-62.
- Kononenko L. I. Relaxations in Singularly Perturbed Planar Systems, Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Ser.: Matematika, Mehanika, Informatika , 2009, vol. 9, no. 4, pp. 45-50.
- Mitropolsky Yu. A., Lykova O. B. Integral'nye mnogoobraziya v nelinejnoj mekhanike , Moscow, Nauka, 1963.
- Vasil'eva A. V., Butuzov V. F. Singulyarno vozmuschennye uravneniya v kriticheskikh sluchayakh , Moscow, Moscow State University, 1978.
- Goldstein V. M., Sobolev V. A. Kachestvennyj analiz singulyarno vozmuschennykh sistem , Novosibirsk, Sobolev Institute of Mathematics, 1988.
- Tikhonov A. N. On Independence of Solutions to Differential Equations on a Small Parameter, Matematicheskij Sbornik , 1948, vol. 22 (64), no. 2, pp. 193-204.
- Kononenko L. I. Direct and Inverse Problems for a Singular System with Slow and Fast Variables in Chemical Kinetics, Vladikavkazskij matematicheskij zhurnal , 2015, vol. 17, no. 1, pp. 39-46 DOI: 10.23671/VNC.2015.1.7291
- Kononenko L. I. Identification Problem for Singular Systems with Small Parameter in Chemical Kinetics, Sibirskie elektronnye matematicheskie izvestiya , 2016, vol. 13, pp. 175-180 DOI: 10.17377/semi.2016.13.015
