Geodesic
A nonlocal problem for fourth-order loaded hyperbolic equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2022), pp. 3-23

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In this paper we consider the nonlocal problem for fourth-order loaded hyperbolic equations with two independent variables. Considered problem is reduced to an equivalent problem, consisting nonlocal problem for a system of loaded hyperbolic equations of second order with functional parameters and integral relations by method introducing new unknown functions. Algorithms for finding solution to the equivalent problem are proposed. Conditions for well-posedness to the nonlocal problem for the system of loaded hyperbolic equations of second order are obtained. Conditions for the existence of unique classical solution to the nonlocal problem for fourth-order loaded hyperbolic equations are established.
Keywords: fourth-order loaded hyperbolic equation, nonlocal problem, system of loaded hyperbolic equations, problem with parameter, algorithm, solvability. 
@article{IVM_2022_8_a0,
     author = {G. A. Abdikalikova and A. T. Assanova and Sh. T. Shekerbekova},
     title = {A nonlocal problem for fourth-order loaded hyperbolic equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--23},
     publisher = {mathdoc},
     number = {8},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_8_a0/}
}
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G. A. Abdikalikova; A. T. Assanova; Sh. T. Shekerbekova. A nonlocal problem for fourth-order loaded hyperbolic equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2022), pp. 3-23. http://geodesic.mathdoc.fr/item/IVM_2022_8_a0/