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On Solvability of Nonlocal Problem for Loaded Parabolic-Hyperbolic Equation

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Abstract

We study unique solvability of a nonlocal problem for equations of mixed type in a finite domain. This equation contains the partial fractional Riemann–Liouville derivative. The boundary condition of the problem contains a linear combination of operators of fractional differentiation in the sense of Riemann–Liouville of values of function derivative on the degeneration line and generalized operators of fractional integro-differentiation in the sense of M. Saigo. The uniqueness theorem of the problem is proved by a modified Tricomi method. The existence of solutions is equivalently reduced to the solvability of Fredholm integral equation of the second kind.

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Authors and Affiliations

  1. Samara State Architecture and Civil Engineering University, ul. Molodogvardeiskaya 194, Samara, 443001, Russia

    A. V. Tarasenko

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  1. A. V. Tarasenko
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Correspondence to A. V. Tarasenko.

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Original Russian Text © A.V. Tarasenko, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 3, pp. 62–69.

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Tarasenko, A.V. On Solvability of Nonlocal Problem for Loaded Parabolic-Hyperbolic Equation. Russ Math. 62, 53–59 (2018). https://doi.org/10.3103/S1066369X18030076

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  • DOI: https://doi.org/10.3103/S1066369X18030076

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