This article is cited in 1 paper

MATHEMATICS

The Goursat problem for a locally loaded equation with a power-law parabolic degeneracy of the second order

A. Kh. Attaev

Institute of Applied Mathematics and Automation, Nalchik

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

UDC: 517.95

Received: 22.11.2024
Revised: 09.12.2024
Accepted: 13.12.2024

DOI: 10.47928/1726-9946-2024-24-4-13-18

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