A problem of the Bitsadze-Samarskii type for a loaded hyperbolic-parabolic equation

  • Khubiev Kazbek U., khubiev_math@mail.ru Institute of Applied Mathematics and Automation KBSC RAS, 89A Shortanov Street, Nalchik, 360000, Russia
Keywords: loaded equation, equation of mixed type, hyperbolic-parabolic equation, nonlocal problem, Bitsadze-Samarskii problem, inner boundary value problem

Abstract

We investigate a problem of the Bitsadze-Samarskii type with inner boundary conditions for a model characteristicly loaded equation of a mixed hyperbolicparabolic type with degeneration of order in the hyperbolic domain. The equation is considered in a mixed domain with a rectangle as the parabolic part and a semi-infinite strip bounded by the characteristics of the wave equation as the hyperbolic part. In the parabolic domain, the equation is a loaded nonhomogeneous heat equation, while it is a loaded nonhomogeneous McKendrick equation in the hyperbolic domain. The function’s values are given on one side of the boundary of the parabolic domain; on the other side of that boundary we give a condition binding the value of the unknown function with the function’s values at the interior points of the its domain. The existence and uniqueness conditions for the regular solution to the problem are determined and the solution representations are written out.

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How to Cite
Khubiev, K. (2019) “A problem of the Bitsadze-Samarskii type for a loaded hyperbolic-parabolic equation”, Mathematical notes of NEFU, 26(2), pp. 31-40. doi: https://doi.org/10.25587/SVFU.2019.102.31510.
Section
Mathematics