On solution of first-order linear systems of partial differential equations
Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 549-563.

Voir la notice de l'article provenant de la source Math-Net.Ru

Explicit formulas for the first-order partial differential equations system solving were obtained. Solution found for the system with initial conditions. Calculation examples establishing statements truth mentioned. Searching for partial differential equations system solution mathematical expectation became more difficult issue as partial differential equations system with random processes coefficients were covered. Gaussian coefficients and uniformly distributed random process cases examples has been reviewed.
@article{CMFD_2021_67_3_a9,
     author = {V. G. Zadorozhniy and L. Yu. Kabantosva},
     title = {On solution of first-order linear systems of partial differential equations},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {549--563},
     publisher = {mathdoc},
     volume = {67},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a9/}
}
TY  - JOUR
AU  - V. G. Zadorozhniy
AU  - L. Yu. Kabantosva
TI  - On solution of first-order linear systems of partial differential equations
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2021
SP  - 549
EP  - 563
VL  - 67
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a9/
LA  - ru
ID  - CMFD_2021_67_3_a9
ER  - 
%0 Journal Article
%A V. G. Zadorozhniy
%A L. Yu. Kabantosva
%T On solution of first-order linear systems of partial differential equations
%J Contemporary Mathematics. Fundamental Directions
%D 2021
%P 549-563
%V 67
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a9/
%G ru
%F CMFD_2021_67_3_a9
V. G. Zadorozhniy; L. Yu. Kabantosva. On solution of first-order linear systems of partial differential equations. Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 549-563. http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a9/

[1] Borovskikh A. V., Perov A. I., Differentsialnye uravneniya, uchebnik i praktikum dlya akademicheskogo bakalavriata, Yurait, M., 2017

[2] Bronshtein I. N., Semendyaev K. A., Spravochnik po matematike dlya inzhenerov i uchaschikhsya vtuzov, Nauka, M., 1986

[3] Zadorozhnii V. G., Metody variatsionnogo analiza, RKhD, M.–Izhevsk, 2006

[4] Zaitsev V. F., Polyanin A. D., Spravochnik po differentsialnym uravneniyam s chastnymi proizvodnymi pervogo poryadka, Fizmatlit, M., 2003

[5] Ilin V. A., Sadovnichii V. A., Sendov B. Kh., Matematicheskii analiz, uchebnik dlya akademicheskogo bakalavriata, Yurait, M., 2018

[6] Koddington E. A., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii, URSS, M., 2010

[7] Kruzhkov S. N., Nelineinye uravneniya s chastnymi proizvodnymi, v. 2, Uravneniya pervogo poryadka, MGU, M., 1970

[8] Kurant R., Uravneniya s chastnymi proizvodnymi, Mir, M., 1964

[9] Petrovskii I. G., Lektsii ob uravneniyakh s chastnymi proizvodnymi, GIFML, M., 1961

[10] Filippov A. F., Sbornik zadach po differentsialnym uravneniyam, Librokom, M., 2013

[11] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. II, Nauka, M., 1970

[12] Shilov G. E., Matematicheskii analiz. Vtoroi spetsialnyi kurs, Fizmatlit, M., 1965

[13] Zadorozhniy V. G., Semenov M. E., Selavesyuk N. T., Ulshin I. I., Nozhkin V. S., “Statistical characteristics of solutions of the system of the stochastic transfer model”, Math. Models Comput. Simul., 13:1 (2021), 11–25 | DOI