A Model Problem for Heat Conduction with a Free Boundary in a Concentrated Capacity

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Abstract
An unconventional free boundary problem of heat conduction is formulated and the theorems of the existence and uniqueness of a classical local solution are proved. The problem models the process of melting (dissolution) of paraffin sediments in a thin porous layer, where a nonisothermal motion of an incompressible liquid is accompanied by the heat exchange with an unbounded impermeable thermally anisotropic medium, and the absorption of a latent heat of fusion (dissolution) occurs at a constant temperature.

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