Geodesic
The analysis and processing of information for one stochastic system of the Sobolev type
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 15 (2023) no. 2, pp. 14-20 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This article is devoted to the analysis and processing of information for a stochastic model based on the equation of potential distribution in a crystalline semiconductor with the Nelson–Glicklich derivative and the Showalter–Sidorov initial condition. By semiconductors, we mean substances that have a finite electrical conductivity that rapidly increases with increasing temperature. It is assumed that the initial experimental data may be affected by random noise, which leads to the study of the stochastic model. An analysis of the stochastic model of the potential distribution in a crystalline semiconductor is given. Conditions under which there are step-by-step solutions of the model under study with the Showalter–Sidorov initial condition are found. Further, on the basis of the theoretical results, an algorithm for the numerical analysis of the system is given. Its implementation is presented in the form of a computational experiment, which is necessary for the further processing of information.
Keywords: stochastic model of potential distribution in a crystalline semiconductor, analysis and processing of information, the Nelson–Glicklich derivative
Mots-clés : Sobolev type equations. 
@article{VYURM_2023_15_2_a1,
     author = {K. V. Perevozchikova},
     title = {The analysis and processing of information for one stochastic system of the {Sobolev} type},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {14--20},
     year = {2023},
     volume = {15},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2023_15_2_a1/}
}
TY  - JOUR
AU  - K. V. Perevozchikova
TI  - The analysis and processing of information for one stochastic system of the Sobolev type
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
PY  - 2023
SP  - 14
EP  - 20
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VYURM_2023_15_2_a1/
LA  - en
ID  - VYURM_2023_15_2_a1
ER  - 
%0 Journal Article
%A K. V. Perevozchikova
%T The analysis and processing of information for one stochastic system of the Sobolev type
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
%D 2023
%P 14-20
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/VYURM_2023_15_2_a1/
%G en
%F VYURM_2023_15_2_a1
K. V. Perevozchikova. The analysis and processing of information for one stochastic system of the Sobolev type. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 15 (2023) no. 2, pp. 14-20. http://geodesic.mathdoc.fr/item/VYURM_2023_15_2_a1/

[1] Da Prato G., Zabczyk J., Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992 | DOI | MR | Zbl

[2] Kovacs M., Larsson S., “Introduction to Stochastic Partial Differential Equations”, Proc. New Directions in the Mathematical and Computer Sciences (National Universities Commission, Abuja, Nigeria, October 8-12, 2007), Publications of the ICMCS, 4, 2008, 2008, 159–232 | Zbl

[3] Zamyshlyaeva A.A., “Stochastic Incomplete Linear Sobolev Type High-Ordered Equations with Additive White Noise”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 40(299):14 (2012), 73–82 | MR | Zbl

[4] Gliklikh Yu.E., Global and Stochastic Analysis with Applications to Mathematical Physics, Springer, N.Y.–London–Dordrecht–Heidelberg, 2011, 436 pp. | DOI | MR | Zbl

[5] Nelson E., Dynamical Theories of Brownian Motion, Princeton University Press, 1967, 142 pp. | MR | Zbl

[6] Shestakov A.L., Sviridyuk G.A., “On the Measurement of the “White Noise””, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 27(286):13 (2012), 99–108 (in Russ.) | Zbl

[7] Shestakov A.L., Sviridyuk G.A., “Optimal Measurement of Dynamically Distorted Signals”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 17(234):5 (2011), 70–75 (in Russ.) | Zbl

[8] Shestakov A.L., Sviridyuk G.A., Hudyakov Yu.V., “Dynamic Measurement in Spaces of “Noise””, Bulletin of the South Ural State University. Series: Computer Technologies, Automatic Control, Radio Electronics, 13:2 (2013), 4–11 (in Russ.)

[9] Favini A., Sviridyuk G.A., Zamyshlyaeva A.A., “One Class of Sobolev Type Equations of Higher Order with Additive “White Noise””, Communications on Pure and Applied Analysis, 15:1 (2016), 185–196 | DOI | MR | Zbl

[10] Favini A., Zagrebina S.A., Sviridyuk G.A., “Multipoint Initial-Final Value Problems for Dynamical Sobolev-Type Equations in the Space of Noises”, Electronic Journal of Differential Equations, 2018:128 (2018), 1–10 | MR

[11] Korpusov M.O., Sveshnikov A.G., “Three-Dimensional Nonlinear Evolution Equations of Pseudoparabolic Type in Problems of Mathematical Physics”, Comput. Math. Math. Phys., 43: 12 (2003), 1765–1797 | MR | Zbl

[12] Manakova N.A., Vasiuchkova K.V., “Research of One Mathematical Model of the Distribution of Potentials in a Crystalline Semiconductor”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 12:2 (2019), 150–157 (in Russ.) | Zbl

[13] Perevochikova K.V., Manakova N.A., Gavrilova O.V., Manakov I.M., “Nonlinear Filtration Mathematical Model with a Random Showalter-Sidorov Initial Condition”, Journal of Computational and Engineering Mathematics, 9:2 (2022), 39–51 | DOI