A~method for solution of a~mixed boundary value problem for a~hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$
Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1227-1254
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{IM2_2023_87_6_a5,
author = {A. Yu. Trynin},
title = {A~method for solution of a~mixed boundary value problem for a~hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$},
journal = {Izvestiya. Mathematics },
pages = {1227--1254},
publisher = {mathdoc},
volume = {87},
number = {6},
year = {2023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a5/}
}
TY - JOUR
AU - A. Yu. Trynin
TI - A~method for solution of a~mixed boundary value problem for a~hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$
JO - Izvestiya. Mathematics
PY - 2023
SP - 1227
EP - 1254
VL - 87
IS - 6
PB - mathdoc
UR - http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a5/
LA - en
ID - IM2_2023_87_6_a5
ER -
%0 Journal Article
%A A. Yu. Trynin
%T A~method for solution of a~mixed boundary value problem for a~hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$
%J Izvestiya. Mathematics
%D 2023
%P 1227-1254
%V 87
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a5/
%G en
%F IM2_2023_87_6_a5
A. Yu. Trynin. A~method for solution of a~mixed boundary value problem for a~hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$. Izvestiya. Mathematics , Tome 87 (2023) no. 6, pp. 1227-1254. http://geodesic.mathdoc.fr/item/IM2_2023_87_6_a5/