This article is cited in 1 paper

A method for solution of a mixed boundary value problem for a hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$

A. Yu. Trynin

Saratov State University

Abstract: A mixed boundary value problem with arbitrary continuous, not necessarily satisfying boundary conditions, functions in initial conditions and inhomogeneities of the equation is solved. A method is proposed for finding a generalized solution by a modification of the interpolation operators of functions constructed from solutions of Cauchy problems with second-order differential expression. Methods of finding the Fourier coefficients of auxiliary functions using the Stieltjes integral or the resolvent of the third-order Cauchy differential operator are proposed.

Keywords: boundary value problem, generalized solution, method of separation of variables.

UDC: 517.518.8

MSC: 34B24, 34L40

Received: 10.04.2022
Revised: 20.10.2022

DOI: 10.4213/im9353

 English version: Izvestiya: Mathematics, 2023, 87:6, 1227–1254

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