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J. Sib. Fed. Univ. Math. Phys., 2021, Volume 14, Issue 2, Pages 133–143 (Mi jsfu898)  

Solvability of BVPs for the parabolic-hyperbolic equation with non-linear loaded term

Obidjon Kh. Abdullaevab

a Romanovsky Institute of Mathematics, Tashkent, Uzbekistan
b National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: This work is devoted to prove the existence and uniqueness of solution of BVP with non-local assumptions on the boundary and integral gluing conditions for the parabolic-hyperbolic type equation involving Caputo derivatives. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of integral equations.

Keywords: Caputo fractional derivatives, loaded equation, integral gluing condition, non-linear integral equation, non-local problem, existence and uniqueness of solution.

DOI: https://doi.org/10.17516/1997-1397-2021-14-2-133-143

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Bibliographic databases:

UDC: 517.956
Received: 10.09.2020
Received in revised form: 10.11.2020
Accepted: 20.02.2021
Language:

Citation: Obidjon Kh. Abdullaev, “Solvability of BVPs for the parabolic-hyperbolic equation with non-linear loaded term”, J. Sib. Fed. Univ. Math. Phys., 14:2 (2021), 133–143

Citation in format AMSBIB
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\by Obidjon~Kh.~Abdullaev
\paper Solvability of BVPs for the parabolic-hyperbolic equation with non-linear loaded term
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2021
\vol 14
\issue 2
\pages 133--143
\mathnet{http://mi.mathnet.ru/jsfu898}
\crossref{https://doi.org/10.17516/1997-1397-2021-14-2-133-143}
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  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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