A Space-Dependent Source Identification Problem for Hyperbolic-Parabolic Equations Maksat Ashyraliyev, Allaberen Ashyralyev, and Victor Zvyagin Abstract In the present paper, a space-dependent source identification problem for the hyperbolic-parabolic equation with unknown parameter p ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ u ′′ (t ) + Au (t ) = p + f (t ), 0 < t < 1, u ′ (t ) + Au (t ) = p + g(t ), − 1 < t < 0, u (0 + ) = u (0 − ), u ′ (0 + ) = u ′ (0 − ), u (−1) = ϕ, 1  0 u (z )dz = ψ in a Hilbert space H with self-adjoint positive definite operator A is investigated. The stability estimates for the solution of this identification problem are established. In applications, the stability estimates for the solutions of four space-dependent source identification hyperbolic-parabolic problems are obtained. Keywords Hyperbolic-parabolic equation · Source identification problem · Stability M. Ashyraliyev (B ) Department of Software Engineering, Bahcesehir University, 34353 Istanbul, Turkey e-mail: maksat.ashyralyyev@eng.bau.edu.tr A. Ashyralyev Department of Mathematics, Near East University, Mersin 10, Nicosia, TRNC, Turkey e-mail: allaberen.ashyralyev@neu.edu.tr Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russian Federation Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan V. Zvyagin Voronezh State University, Universitetskaya 1, Voronezh 394018, Russia e-mail: zvg_vsu@mail.ru © Springer Nature Switzerland AG 2021 A. Ashyralyev et al. (eds.), Functional Analysis in Interdisciplinary Applications—II, Springer Proceedings in Mathematics & Statistics 351, https://doi.org/10.1007/978-3-030-69292-6_14 183