Abstract
We consider mathematical modeling of problems with free boundaries, namely, the investigation of the Stefan type problem with a non-constant melting point, taking into account the pressure in the liquid phase. A mathematical model has been constructed that describes the melting process of heavy paraffin-base crude oil. We prove an existence and uniqueness of a solution of a Stefan-type problem in the Holder spaces with a melting point that depends on the unknown pressure are considered. We study the solvability in Holder spaces and the asymptotic behavior for t, which tends to ∞, solving a single-phase Stefan-type problem for a nonlinear parabolic equation.
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