Geodesic
Boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2020), pp. 3-14

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

We consider a boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition on rectangular domain. By introducing new unknown function considered problem is reduced to equivalent nonlocal problem with integral condition for system of hyperbolic integro-differential equations of the second order. Algorithm for finding of approximate solution to equivalent problem is proposed and its convergence is proved on the basis method of functional parametrization. Sufficient conditions of the existence unique classical solution to boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition are established in the terms of initial data.
Keywords: system of pseudo-hyperbolic equations, nonlocal problem, system of hyperbolic integro-differential equations, integral condition, solvability. 
@article{IVM_2020_9_a0,
     author = {A. T. Assanova and Zh. S. Tokmurzin},
     title = {Boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--14},
     publisher = {mathdoc},
     number = {9},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_9_a0/}
}
TY  - JOUR
AU  - A. T. Assanova
AU  - Zh. S. Tokmurzin
TI  - Boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2020
SP  - 3
EP  - 14
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2020_9_a0/
LA  - ru
ID  - IVM_2020_9_a0
ER  - 
%0 Journal Article
%A A. T. Assanova
%A Zh. S. Tokmurzin
%T Boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2020
%P 3-14
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2020_9_a0/
%G ru
%F IVM_2020_9_a0
A. T. Assanova; Zh. S. Tokmurzin. Boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2020), pp. 3-14. http://geodesic.mathdoc.fr/item/IVM_2020_9_a0/