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8the pseudo-trajectories, including round-off errors, leads to the actual study of the trajectory with some ap-
proximation. The report proposes to use pseudo-trajectories to consider the data space as a space of problems
and to estimate the relationship between a defect, local and global errors of numerical solutions. Examples of
numerical estimates of the global error are given.
This work was carried out within the framework of the state assignment of the Federal Research Center of the KSC
SB RAS, project No. 0287-2021-0002.
References
1. Rogalev A. N., Feodorova N.A. Regularization of algorithms for estimation of errors of differential equations
approximate solutions // J. of Physics: Conference Series 1715 (2021) 012044 doi:10.1088/1742-6596/1715/1/012044.
Kinetic modeling of propane pyrolysis: parameters identifiability and estimation
L. F. Safiullina1, I. M. Gubaydullin2
1Bashkir State University, Ufa
2Institute of Petrochemistry and Catalysis UFRC RAS
Email: SafiullinaLF@gmail.com
DOI 10.24412/cl-35065-2021-1-02-10
One of heavy olefins upgrading processes is pyrolysis. As it is a complex process involving many chemical
reactions, the mathematical model of pyrolysis process often has more kinetic parameters than can be esti-
mated from the data. In this article, a kinetic model for propane pyrolysis processing is proposed. It is proved
that the model is practically identifiable. Practical identifiability analysis is based on simulated model outputs
and their sensitivities with respect to parameters [1, 2]. As a result of the analysis of identifiability, the least
and most sensitive parameters to measurements were identified. The minimization problem was solved
through the genetic algorithm method that is widely applied for stochastic global optimization. It has been
demonstrated that kinetic model describes the experimental data of the observed substances of the reaction.
The reported study was funded by RFBR, project number 19-37-60003.
References
1. Yao K.Z., Shaw B.M., Kou B., McAuley K.B., Bacon D.W. Modeling ethylene/butene copoly-merization with
multi-site catalysts: parameter estimability and experimental design. Polymer Reaction Engineer. 2003.11(3). 563-588.
2. Safiullina L.F., Gubaydullin I.M. Numerical analysis of parameter identifiability for a mathematical model of a
chemical reaction. International J. of Engineering Systems Modelling and Simulation. 2020. 11(4). 207-213.
Multiplicative control problems for semilinear reaction-diffusion-convection equation
Zh. Yu. Saritskaia1,2, R. V. Brizitskii1,2
1Institute of Applied Mathematics FEB RAS
2Far Eastern Federal University, Vladivostok
Email: zhsar@icloud.com, mlnwizard@mail.ru
DOI 10.24412/cl-35065-2021-1-02-11
The interest in the study of boundary value and control problems for linear as well as for nonlinear models
for mass and heat transfer does not fade over sufficiently long time (see [1, 2] and References in there). In this
paper, we consider multiplicative control problems for the semilinear reaction-diffusion-convection equation.
The coefficients in both the equation and the boundary condition of the model under consideration depend on
the solution of the boundary value problem (see [2]). The diffusion coefficient plays a role of a multiplicative
control. The solvability of a multiplicative control problem under consideration was proved in [2]. For concrete
reaction and mass transfer coefficients we obtain optimality systems and based on their analysis we establish
local stability estimates for optimal solutions.
This work was carried out in the framework of the State Order for the Institute of Applied Mathematics of the Far
East Branch of the Russian Academy of Science, topic no. 075-01095-20-00.
References
1. Brizitskii R. V., Saritskaya Zh. Yu. Optimization analysis of the inverse coefficient problem for the nonlinear
convection-diffusion-reaction equation // J. Inv. Ill-Posed Probl. 2018. V. 26, N 6. P. 821-833.
2. Brizitskii R. V., Bystrova V. S., Saritskaia Zh. Yu. Analysis of boundary value and extremum problems for a nonlinear
reaction-diffusion-convection equation // Differential Equation. 2021. V. 57, N 5. P. 615-629.
On the inverse boundary value problem solution for parabolic equation in a cylindrical coordinate system
A. I. Sidikova
South Ural State University, Chelyabinsk
Email: sidikovaai@susu.ru
DOI 10.24412/cl-35065-2021-1-02-12
This work solves the problem the inner wall temperature determination of a hollow cylinder consisting of
composite materials. The problem is reduced to an ordinary differential equation using the Fourier transform
in time and the Fourier transform is found for the exact solution of the desired inverse boundary value
problem.
The projection regularization method [1] is used to solve it. This method makes it possible to obtain a sta-
ble solution to the problem and to estimate the error of the approximate solution. Working with Bessel func-
tions [2] complicates the technique of obtaining the error estimate. This problem is of known interest in con-
nection with the theory of thermocouples and devices for measuring current.
The work was supported by the Ministry of Science and Higher Education of the Russian Federation (government or-
der FENU-2020-0022).
References
1. V.K. Ivanov, V. V. Vasin and V.P. Tanana Theory of Linear Ill-Posed problems and its Applications. The Netherlands,
VSP, 2002.
2. Gray A., Mathews G.B. A Treatise on Bessel Functions and their Applications to Physics. M.: Nauka 1953.
Direct method for solving the problem of identifying the coefficients of an elliptic equation
S. B. Sorokin
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Novosibirsk State University
Email: sorokin@sscc.ru
DOI 10.24412/cl-35065-2021-1-02-13
A direct method for solving the inverse coefficient problem for an elliptic equation with piecewise con-
stant coefficients is presented. The method allows much faster, in comparison with the implementation of it-
erative procedures for this problem, to restore the unknown coefficients of thermal conductivity. The values
(measurements) of the solution at the break points of the coefficients are used as additional information.
