Abstract
For a hyperbolic system with simple characteristics in the \(n \)-dimensional space of independent variables, the existence and uniqueness of a solution of the Darboux problem is proved. The Riemann–Hadamard matrix is determined, and the solution of the Darboux problem is constructed in terms of this matrix. As an example of application of the results, the solution of the Darboux problem for a system with four independent variables is constructed in detail.
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This paper has been supported by the Kazan Federal University Strategic Academic Leadership Program.
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Translated by V. Potapchouck
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Mironov, A.N., Mironova, L.B. On the Darboux Problem for Hyperbolic Systems. Diff Equat 59, 654–663 (2023). https://doi.org/10.1134/S0012266123050087
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DOI: https://doi.org/10.1134/S0012266123050087