Geodesic
On a nonlocal boundary value problem for a model hyperbolic nonlocal equations
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 40 (2022) no. 3, pp. 7-15

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The paper studies the problem with internal-boundary non-characteristic displacement for a model heavily loaded second-order hyperbolic type equation with two independent variables. We emphasize that for loaded hyperbolic equations with the load being characteristic, the main initial and boundary value problems are formulated as well as for ordinary equations. But if we deal with a non-characteristic load, then the task is reduced to the correct choice among the manyfold inherent in the initial, boundary, and mixed data. An analogue of the mean value theorem and an analogue of the d'Alembert formula are given. To solve the problem, the d0Alembert method is used.
Keywords: heavily loaded differential equation, internal-boundary noncharacteristic displacement, mean value theorem, d′Alembert′s method, functional equation, characteristics of a hyperbolic equation. 
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     author = {A. Kh. Attaev},
     title = {On a nonlocal boundary value problem for a model hyperbolic nonlocal equations},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {7--15},
     publisher = {mathdoc},
     volume = {40},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2022_40_3_a0/}
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A. Kh. Attaev. On a nonlocal boundary value problem for a model hyperbolic nonlocal equations. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 40 (2022) no. 3, pp. 7-15. http://geodesic.mathdoc.fr/item/VKAM_2022_40_3_a0/