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On Solution of First-Order Linear Systems of Partial Differential Equations

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Abstract

Explicit formulas for solving a system of first-order partial differential equations are obtained. The solution of the system with initial conditions is found. Examples of calculations are given to show the truth of the statements. The more difficult problem was to find the mathematical expectation of a solution for the system of partial differential equations whose coefficients are random processes. An example with Gaussian coefficients is considered.

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Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    V. G. Zadorozhniy & L. Yu. Kabantsova

Authors
  1. V. G. Zadorozhniy
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  2. L. Yu. Kabantsova
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Correspondence to V. G. Zadorozhniy.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 3, In honor of the 70th anniversary of Professor V. M. Filippov, 2021.

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Zadorozhniy, V.G., Kabantsova, L.Y. On Solution of First-Order Linear Systems of Partial Differential Equations. J Math Sci 278, 328–341 (2024). https://doi.org/10.1007/s10958-024-06923-6

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  • DOI: https://doi.org/10.1007/s10958-024-06923-6

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