CC BY
7problem to a set of linear integral equations. We study the possibility to use the method in case of general
time form of the sounding wave. In 2D case we also consider the modification of the method that uses the da-
ta, obtained by the areal data collection system. The results of numerical experiments are presented.
This work has been supported by the Russian Science Foundation under grant 20-71-00128 "Development of new al-
gorithms for parameters identification of geophysics based on the direct methods of data processing".
References
1. Kabanikhin, S.I., Novikov, N.S., Oseledets, I.V., Shishlenin, M.A., Fast Toeplitz linear system inversion for solving
two-dimensional acoustic inverse problem, Journal of Inverse and Ill-Posed Problems, 2015, v. 23 N. 5. P. 687�700.
2. Kabanikhin, S.I., Sabelfeld, K.K., Novikov, N.S., Shishlenin, M.A., Numerical solution of the multidimensional
Gelfand-Levitan equation, Journal of Inverse and Ill-Posed Problems, 2015, v. 23. N. 5. P. 439-450.
3. Kabanikhin, S.I., Sabelfeld, K.K., Novikov, N.S., Shishlenin, M.A., Numerical solution of an inverse problem of
coefficient recovering for a wave equation by a stochastic projection methods, Monte Carlo Methods and Applications,
2015. V. 21, N. 3. P. 189�203.
Mean field games for modeling of disease propagation
V. Petrakova1, O. Krivorotko2,3
1Institute of Computational Modelling SB RAS, Krasnoyarsk
2Institute of Computational Mathematics and Mathematical Geophysics SB RAS
3Novosibirsk State University
Email: vika-svetlakova@yandex.ru
DOI 10.24412/cl-35065-2021-1-03-05
The mean field game (MFG) that describes the control of a population with a large number of interacting
agents [1] is numerically investigated. MFG is based on Kolmogorov (Fokker � Planck) equations that charac-
terize the distributions of agents in four groups (susceptible, infected; recovered and cross-immune people)
and system of Hamilton-Jacobi-Bellman equations that describes the optimal strategy of isolation: if a person
is not infected and the number of non-isolating people in population is arising, person's profit decreases to
comply with the restrictions. Otherwise, if a person is infected, then he is inclined to comply with restrictions.
The optimality conditions are derived. The scenarios of COVID-19 propagation in Siberia depend on restrictions
[2] are modelled and discussed.
This work is supported by the Russian Science Foundation (grant no. 18-71-10044).
References
1. J.-M. Lasry and P.-L. Lions. Mean field games. Jpn. J. Math. 2007. V. 2, N. 1. P. 229-260.
2. O.I. Krivorotko, S.I. Kabanikhin, N.Yu. Zyatkov, et al. Mathematical modeling and forecasting of COVID-19 in Mos-
cow and Novosibirsk region. Numerical Analysis and Applications. 2020. V. 13, N. 4. P. 332-348.
On the singular value decomposition of the ray transforms operators acting on 2D tensor fields
A. P. Polyakova, I. E. Svetov
Sobolev Institute of Mathematics SB RAS
Email: apolyakova@math.nsc.ru
DOI 10.24412/cl-35065-2021-1-02-06
We consider the problem of the 2D m-tensor tomography. Namely, it is necessary to reconstruct a 2D
symmetric m-tensor field by values of its ray transforms. We propose to solve the problem with usage of the
singular value decomposition method. The singular value decompositions of the ray transforms operators act-
ing on vector and 2-tensor fields were constructed earlier [1, 2].
This research was partially supported by RFBR and DFG according to the research project 19-51-12008.
References
1. Derevtsov E. Yu., Efimov A. V., Louis A. K. and Schuster T. Singular value decomposition and its application to
numerical inversion for ray transforms in 2D vector tomography. J. of Inverse and Ill-posed Problems. 2011. V. 19, No 4�5.
P. 689�715.
2. Derevtsov E. Yu., Polyakova A. P. Solution of the Integral Geometry Problem for 2-Tensor Fields by the Singular
Value Decomposition Method. J. of Mathematical Sciences. 2014. V. 202, No 1. P. 50�71.
On the singular value decomposition of the dynamic ray transforms operators acting on 2D tensor fields
A. P. Polyakova1, I. E. Svetov1, B. Hahn2
1Sobolev Institute of Mathematics SB RAS
2University of Wurtzburg, Germany
Email: apolyakova@math.nsc.ru
DOI 10.24412/cl-35065-2021-1-02-07
We consider the problems of the dynamic 2D vector and 2-tensor tomography. The initial data are values
of the longitudinal and/or transverse and/or mixed dynamic ray transforms. An object motion is known and
consist of rotation and shifting [1]. Properties of the dynamic ray transforms operators are investigated. The
singular value decompositions of the operators with usage of the classic orthogonal polynomials are con-
structed [2, 3].
This research was partially supported by RFBR and DFG according to the research project 19-51-12008.
References
1. Hahn B. Null space and resolution in dynamic computerized tomography. Inverse Problems. 2016. V. 32, No 2,
025006.
2. Polyakova A. P., Svetov I. E., Hahn B. N. The Singular Value Decomposition of the Operators of the Dynamic Ray
Transforms Acting on 2D Vector Fields. Lect. Notes in Computer Science. 2020. V. 11974. P. 446�453.
3. Polyakova A. P., Svetov I.E. The singular value decomposition of the dynamic ray transforms operators acting on
2-tensor fields in R2. J. of Physics: Conference Series. 2021. V. 1715. 012040.
Regularization methods for solving the continuation problem
A. Prikhodko1,2, M. Shishlenin1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS
2Novosibirsk State University
Email: a.prikhodko@g.nsu.ru
DOI 10.24412/cl-35065-2021-1-03-08
When conducting experiments for heat and mass transfer, the main studied values are the heat flux densi-
ty and temperature. The most commonly used field and local methods that have high accuracy, in particular
infrared thermography.
There are no direct methods for measuring the heat flux density at a distance. There is a need to estimate
the flow density from temperature measurements.
