On a heat and mass transfer model for the locally inhomogeneous initial data
Tynysbek Sh. Kalmenov, Gaukhar D. Arepova · AIP conference proceedings · 2016
In this paper we consider a model case of the problem of heat (or mass) 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 Ω inside a body such that the initial state is constant out of the domain. Mathematical modeling leads to the problem for a homogeneous multi-dimensional diffusion equation. We construct the boundary conditions on the boundary of the domain Ω, which can be characterized as ”transparent” boundary conditions. We separately consider a special case, that is, a model of redistribution of heat (or mass) in a uniform linear rod, the side surface of which is insulated in the absence of (internal and external) sources of heat (or mass) and of locally inhomogeneous initial state.