Abstract
Unique solvability of the one-phase Stefan problem with a small multiplier ε at the time derivative in the equation is proved on a certain time interval independent of ε for ε ∈ (0, ε0). The solution to the Stefan problem is compared with the solution to the Hele-Show problem, which describes the process of melting materials with zero specific heat ε and can be regarded as a quasistationary approximation for the Stefan problem. It is shown that the difference of the solutions has order \( \mathcal{O}(\varepsilon ) + \mathcal{O}(e^{ - \tfrac{{ct}} {\varepsilon }} ) \) . This provides a justification of the quasistationary approximation. Bibliography: 23 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 209–253.
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Solonnikov, V.A., Forolova, E.V. Justification of a quasistationary approximation for the Stefan problem. J Math Sci 152, 741–768 (2008). https://doi.org/10.1007/s10958-008-9091-6
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DOI: https://doi.org/10.1007/s10958-008-9091-6