Abstract:
This article is devoted to the study of an inverse source problem for a mixed type equation with a fractional diffusion equation in the parabolic part and a wave equation in the hyperbolic part of a cylindrical domain. The solution is obtained
in the form of Fourier–Bessel series expansion using an orthogonal set of Bessel functions.
The theorems of uniqueness and existence of a solution are proved.
Keywords:
inverse problem, equation of mixed type, Fourier–Bessel series, Mittag–Leffler function, uniqueness and existence.
Citation:
D. K. Durdiev, “Inverse source problem for an equation of mixed parabolic-hyperbolic type with the time fractional derivative in a cylindrical domain”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 26:2 (2022), 355–367
\Bibitem{Dur22}
\by D.~K.~Durdiev
\paper Inverse source problem for an equation of mixed parabolic-hyperbolic type with the time fractional derivative in a cylindrical domain
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2022
\vol 26
\issue 2
\pages 355--367
\mathnet{http://mi.mathnet.ru/vsgtu1921}
\crossref{https://doi.org/10.14498/vsgtu1921}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4494667}
\edn{https://elibrary.ru/TWHCKX}
Linking options:
https://www.mathnet.ru/eng/vsgtu1921
https://www.mathnet.ru/eng/vsgtu/v226/i2/p355
This publication is cited in the following 4 articles:
Citation in format AMSBIB
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