Geodesic
On the justification of the quasistationary approximation
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 209-253 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove the unique solvability of the one-phase Stefan problem with a small multiplier $\varepsilon$ at the time derivative in the equation on a certain time interval independent of $\varepsilon$ for $\varepsilon\in (0,\varepsilon_0)$. We compare the solution to the Stefan problem with the solution to the Hele-Show problem which describes the process of melting materials with zero specific heat $\varepsilon$ and can be considered as a quasistationary approximation for the Stefan problem. We show that the difference of the solutions has order $\mathcal O(\varepsilon)+\mathcal O(e^{-\frac{ct}{\varepsilon}})$. This provides justification of the quasistationary approximation. 
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V. A. Solonnikov; E. V. Frolova. On the justification of the quasistationary approximation. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 209-253. http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a7/

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