Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 40. no. 3. pp. 7–15. ISSN 2079-6641

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MSC 35L10

Research Article

On a nonlocal boundary value problem for a model hyperbolic nonlocal equations

A. Kh. Attaev

Institute of Applied Mathematics and Automation KBSC RAS, 89А, Shortanova St., Nalchik, 360000, Russia


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.

Key words: heavily loaded differential equation, internal-boundary noncharacteristic displacement, mean value theorem, d′Alembert′s method, functional equation, characteristics of a hyperbolic equation.

DOI: 10.26117/2079-6641-2022-40-3-7-15

Original article submitted: 16.10.2022

Revision submitted: 20.11.2022

For citation. Attaev A. Kh. On a nonlocal boundary value problem for a model hyperbolic
nonlocal equations. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 40: 3, 7-15. DOI:

Competing interests. The author declares that there are no conflicts of interest with
respect to authorship and publication.

Contribution and responsibility. The author contributed to the writing of the article and is solely responsible for submitting the final version of the article to the press. The final version of the manuscript was approved by the author.

The content is published under the terms of the Creative Commons Attribution 4.0 International License (

© Attaev A. Kh., 2022


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Attaev Anatoly Khuseievich – Ph.D. (Phys. & Math.), Head of Department «Equations of Mixed Type», Institute of Applied Mathematics and Automation, Kabardino-Balkarian Republic, Nalchik, Russia, ORCID 0000-0001-5864-6283