Geodesic
The Dirichlet problem for telegraph equation in a rectangular domain
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2017), pp. 46-56

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate the Dirichlet problem for telegraph equation in rectangular domain. We establish a criterion of uniqueness. The solution to the problem is constructed in the form of the sum of orthogonal series. In substantiation of convergence of the series there appears the problem of small denominators. In connection with this we establish the estimates of separation from zero of denominators with the corresponding asymptotics which allow to substantiate the existence of a regular solution and prove its stability depending on boundary functions.
Keywords: telegraph equation, the Dirichlet problem, spectral method, criterion of uniqueness, small denominators, stability. 
@article{IVM_2017_12_a4,
     author = {Yu. K. Sabitova},
     title = {The {Dirichlet} problem for telegraph equation in a rectangular domain},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {46--56},
     publisher = {mathdoc},
     number = {12},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_12_a4/}
}
TY  - JOUR
AU  - Yu. K. Sabitova
TI  - The Dirichlet problem for telegraph equation in a rectangular domain
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 46
EP  - 56
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_12_a4/
LA  - ru
ID  - IVM_2017_12_a4
ER  - 
%0 Journal Article
%A Yu. K. Sabitova
%T The Dirichlet problem for telegraph equation in a rectangular domain
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 46-56
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_12_a4/
%G ru
%F IVM_2017_12_a4
Yu. K. Sabitova. The Dirichlet problem for telegraph equation in a rectangular domain. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2017), pp. 46-56. http://geodesic.mathdoc.fr/item/IVM_2017_12_a4/