Geodesic
On an initial-boundary-value problem for a fourth-order system of loaded differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 3-21

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

In this paper, we consider an initial-boundary-value problem for a system of loaded fourth-order differential equations. By introducing additional unknown functions, we reduce the problem to an equivalent problem for a system of loaded second-order hyperbolic equations with functional parameters and integral relations and propose algorithms for solving this problem. Solvability conditions of a nonlocal multipoint problem for a system of loaded second-order hyperbolic equations are set up. Moreover, conditions for the existence of a unique classical solution to the initial-boundary-value problem for a system of loaded differential equations of the fourth order are established.
Keywords: initial-boundary-value problem, system of loaded fourth-order differential equations, nonlocal problem, system of loaded hyperbolic equations. 
@article{INTO_2021_198_a0,
     author = {A. T. Assanova and Sh. T. Shekerbekova},
     title = {On an initial-boundary-value problem for a fourth-order system of loaded differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--21},
     publisher = {mathdoc},
     volume = {198},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_198_a0/}
}
TY  - JOUR
AU  - A. T. Assanova
AU  - Sh. T. Shekerbekova
TI  - On an initial-boundary-value problem for a fourth-order system of loaded differential equations
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2021
SP  - 3
EP  - 21
VL  - 198
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2021_198_a0/
LA  - ru
ID  - INTO_2021_198_a0
ER  - 
%0 Journal Article
%A A. T. Assanova
%A Sh. T. Shekerbekova
%T On an initial-boundary-value problem for a fourth-order system of loaded differential equations
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2021
%P 3-21
%V 198
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2021_198_a0/
%G ru
%F INTO_2021_198_a0
A. T. Assanova; Sh. T. Shekerbekova. On an initial-boundary-value problem for a fourth-order system of loaded differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 3-21. http://geodesic.mathdoc.fr/item/INTO_2021_198_a0/