Abstract
We study some questions of the qualitative theory of differential equations. A Cauchy problem is considered for a hyperbolic system of two first-order differential equations whose right-hand sides contain some discontinuous functions. A generalized solution is defined as a continuous solution to the corresponding system of integral equations. We prove the existence and uniqueness of a generalized solution and study the differential properties of the obtained solution. In particular, its first-order partial derivatives are unbounded near certain parts of the characteristic lines. We observe that this property contradicts the common approach which uses the reduction of a system of two first-order equations to a single second-order equation.
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Original Russian Text © D.S. Anikonov, S.G. Kazantsev, D.S. Konovalova, 2013, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2013, Vol. XVI, No. 2, pp. 26–39.
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Anikonov, D.S., Kazantsev, S.G. & Konovalova, D.S. Differential properties of a generalized solution to a hyperbolic system of first-order differential equations. J. Appl. Ind. Math. 7, 313–325 (2013). https://doi.org/10.1134/S1990478913030046
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DOI: https://doi.org/10.1134/S1990478913030046