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This article is cited in 3 scientific papers (total in 3 papers)
Short Communication
The Bitsadze–Samarskii problem for some characteristically loaded hyperbolic-parabolic equation
K. U. Khubiev Institute of Applied Mathematics and Automation
of Kabardin-Balkar Scientific Centre of RAS,
Nal’chik, 360000, Russian Federation.
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
The paper considers a characteristically loaded equation of a mixed hyperbolic-parabolic type with degeneration of order in the hyperbolicity part of the domain. In the hyperbolic part of the domain, we have a loaded one-velocity transport equation, known in mathematical biology as the Mac Kendrick Von Forester equation, in the parabolic part we have a loaded diffusion equation. The purpose of the paper is to study the uniqueness and existence of the solution of the nonlocal inner boundary value problem with Bitsadze-Samarskii type boundary conditions and the continuous conjugation conditions in the parabolic domain; the hyperbolic domain is exempt from the boundary conditions.
The problem under investigation is reduced to a non-local problem for an ordinary second-order differential equation with respect to the trace of the unknown function in the line of the type changing. The existence and uniqueness theorem for the solution of the problem has been proved; the solution is written out explicitly in the hyperbolic part of the domain. In the parabolic part, the problem under study is reduced to the Volterra integral equation of the second kind, and the solution representation has been found.
Keywords:
loaded equation, equation of mixed type, hyperbolic-parabolic equation, nonlocal problem, Bitsadze–Samarskii problem, internal boundary value problem.
Received: February 15, 2019 Revised: August 29, 2019 Accepted: November 11, 2019 First online: December 23, 2019
Citation:
K. U. Khubiev, “The Bitsadze–Samarskii problem for some characteristically loaded hyperbolic-parabolic equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:4 (2019), 789–796
Linking options:
https://www.mathnet.ru/eng/vsgtu1677 https://www.mathnet.ru/eng/vsgtu/v223/i4/p789
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