Geodesic
On a heat and mass transfer model for the locally inhomogeneous initial data
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 124-129

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We consider a model case of the problem of heat diffusion in a homogeneous body with a special initial state. The peculiarity of this initial state is its local inhomogeneity. That is, there is a closed domain $\Omega$ inside a body, the initial state is constant out of the domain. Mathematical modelling leads to the problem for a homogeneous multi-dimensional diffusion equation. We construct the boundary conditions on the boundary of the domain $\Omega$, which can be characterized as "transparent" boundary conditions. We separately consider a special case — a model of redistribution of heat in a uniform linear rod, the side surface of which is insulated in the absence of (internal and external) sources of heat and of locally inhomogeneous initial state.
Keywords: diffusion equation; homogeneous body; initial state; local inhomogeneity; transparent boundary conditions. 
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     author = {T. Sh. Kal'menov and G. D. Arepova},
     title = {On a heat and mass transfer model for the locally inhomogeneous initial data},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {124--129},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a11/}
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T. Sh. Kal'menov; G. D. Arepova. On a heat and mass transfer model for the locally inhomogeneous initial data. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 124-129. http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a11/