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Telecommunications and Radio Engineering
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ISSN Druckformat: 0040-2508
ISSN Online: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v54.i8-9.10
pages 2-13

Dissipative Phenomena in Boundary-value Problems of Linear Magnetic Hydrodynamics

Alevtina Alexandrovna Aleksandrova
Kharkov National University of Radio Engineering and Electronics, 14, Lenin Ave, Kharkov, 61166, Ukraine
Nikolai Antonovich Khizhnyak
V. Karazin National University of Kharkov, Ukraine


The purpose of this work is to develop a modern theoretical basis for the solution of self-consistent magnetohydrodynamic (MHD) boundary-value problems. The necessary generality of the method offered can be achieved by developing it on the basis of an integral formulation combining the field equations and the medium motion equations. The obtaining of the Green's function for a linear MHD medium and deriving on its basis the integral equation in a laboratory coordinate system is the essential point of the method.
The advantages of the integral equations lie in their physical clarity, possibility to represent the solutions of many boundary-value problems in a closed analytical form and to reduce the solution to stable numerical algorithms, and the compact formulation of boundary-value problems for continuous anisotropic media.
The new formalism will allow us to solve effective problems concerning the reflection of MHD waves by fixed and movable, single and multiple discontinuities in anisotropic MHD media. In this paper, we give detailed results for the refraction of waves in a particular case, when there are no disturbed movements of the media; that is, we consider the influence of dissipative phenomena on the wave refraction. We also consider another particular case, in which magnetic viscosity is equal to zero, but the initial motion of the internal medium has a velocity U0.

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