Mathematical modeling

On the Riemann-Hadamard method for Bianchi equations

A. N. Mironov

Kazan (Volga Region) Federal University

Abstract: A method for constructing explicit solutions to Darboux problems for Bianchi equations is considered, which is a generalization of the Riemann-Hadamard method for a secondorder hyperbolic equation. The definition of the Riemann - Hadamard function for the Bianchi equation in the general case is given. The existence and uniqueness of the solution of the Darboux problems for the Bianchi equations is proved by reduction to the Volterra integral equation with partial integrals.

Keywords: Bianchi equation, Darboux problem, Riemann — Hadamard method, Riemann — Hadamard function

UDC: 517.956

DOI: 10.25587/2411-9326-2025-2-92-93