Inverse source problem for an equation of mixed parabolic-hyperbolic type with the time fractional derivative in a cylindrical domain

D. K. Durdiev

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 26 (2022) no. 2, pp. 355-367.

Résumé

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.

Détail

Keywords: inverse problem, equation of mixed type, Fourier–Bessel series, Mittag–Leffler function, uniqueness and existence.

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