Adyghe Int. Sci. J. Vol. 24, No. 4. P. 13–18.
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DOI: https://doi.org/10.47928/1726-9946-2024-24-4-13-18
EDN: LVMONJ
MATHEMATICS
MSC 35L10 | Original Article |
The Goursat problem for a locally
loaded equation with a power-law parabolic degeneracy of the second order
Anatoly Khuseevich Attaev
Candidate of Physical and Mathematical Sciences, a leading researcher at the Department of Mixed-type Equations at the Research Institute of Applied Mathematics and Automation KBSC RAS (360000, Kabardino-Balkarian Republic, Nalchik, 89A Shortanov St.), ORCID: https://orcid.org/0000-0001-5864-6283, attaev.anatoly@yandex.ru
Abstract. A loaded degenerate second-order hyperbolic equation is considered, which, under certain physical constraints on the parameters included in it, describes the process of moisture transfer in porous media. The loaded term is a trace of the desired solution on the line of degeneracy of this equation and lies completely inside the area under consideration. The mapping that forms this trace is a hatracteristic one. A problem with data that is set on one of the characteristics of this equation is investigated. The existence and uniqueness of the task are proved, and its solution is written out explicitly.
Keywords: a mixed type equation, the process of moisture transfer, the line of degeneration, Gursa’s task.
Funding. This work was carried out within the framework of the state assignment of the Ministry of Education and Science of the Russian Federation under the project: Boundary value and control problems for basic and mixed types of equations and their application to the study of systems with distributed parameters (1021032421196-2).
Competing interests. There are no conflicts of interest regarding authorship and publication.
Contribution and Responsibility. The author participated in the writing of the article and is fully responsible for submitting the final version of the article to the press.
For citation. Attaev A. Kh. The Goursat problem for a locally loaded equation with a power-law parabolic degeneracy of the second order. Adyghe Int. Sci. J. 2024. Vol. 24, No. 4. Pp. 13–18.
DOI: https://doi.org/10.47928/1726-9946-2024-24-4-13-18; EDN: LVMONJ
Submitted 22.11.2024; approved after reviewing 09.12.2024; accepted for publication 13.12.2024.
© Attaev A. Kh., 2024
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