This article is cited in 2 papers

MATHEMATICS

Remarks on the recovery of solutions of initial boundary value problems for singularwave equations

M. V. Polovinkina^a, I. P. Polovinkin<sup>b

a</sup> Voronezh State University of Engineering Technologies
^b Voronezh State University; Belgorod State National Research University

Abstract: The paper deals with a mixed problem for a second-order hyperbolic equation with two variables (one spatial variable and one time variable) with the Bessel operator. It is assumed that the first few coefficients of the expansion of the initial function into a Fourier series by Bessel functions are known. The case of the classical expansion of the initial function by the sines of multiple arcs, when the Bessel operator acts only with respect to the time variable, is considered separately. The problem of recovery of the solution based on these data is considered. The paper uses the results and methods presented in the works by G. G. Magaril-Il'yaev, K. Yu. Osipenko, E. O. Sivkova, N. D. Vysk.

Keywords: bessel operator, bessel functions, recovery method, initial boundary value problem, wave equation.

Received: 30.12.2023
Accepted: 30.12.2023

DOI: 10.52575/2687-0959-2023-55-4-330-338