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.

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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. 
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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/

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