Inverse problem for a hyperbolic integro-differential equation in a bounded domain
Read more
In this paper, we consider the inverse problem of determining the kernel of an integral term in an integro-differential equation. The problem of determining the memory kernel in the wave process is reduced to a nonlinear Volterra integral equation of the first kind of convolution type, then over determination condition it brings to the Volterra integral equation of the second kind. The method of contraction maps proves the unique solvability of the problem in the space of continuous functions with weight norms, and an estimate of the conditional stability of the solution is obtained
УДК 517.958
Keywords: integro-differential equation, inverse problem, kernel, spectral problem, fixed point theorem, Gronwall inequality
0000-0001-9249-835X The material was received by the Editorial Board: 18.01.2023
In this paper, we consider the inverse problem of determining the kernel of an integral term in an integro-differential equation. The problem of determining the memory kernel in the wave process is reduced to a nonlinear Volterra integral equation of the first kind of convolution type, then over determination condition it brings to the Volterra integral equation of the second kind. The method of contraction maps proves the unique solvability of the problem in the space of continuous functions with weight norms, and an estimate of the conditional stability of the solution is obtained
УДК 517.958
Keywords: integro-differential equation, inverse problem, kernel, spectral problem, fixed point theorem, Gronwall inequality
References: Safarov J. Sh., Durdiev D. K., Rakhmonov A. A. Inverse problem for a hyperbolic integro-differential equation in a bounded domain. Mat. Trudy. 2024, 27, № 1. P. 139–162. DOI: 10.25205/1560-750X-2024-27-1-139-162