The order of convergence in the Stefan problem with vanishing specific heat
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Tome 385 (2010), pp. 206-223
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The paper is concerned with a two-phase Stefan problem with a small parameter $\varepsilon$ which coresponds to the specific heat of the material. We assume that the initial condition does not coincide with the value at $t=0$ of the solution to the limit problem related to $\varepsilon=0$. To remove this discrepancy, we introduce an auxiliary boundary layer type function. We prove that the solution to the two-phase Stefan problem with parameter $\varepsilon$ differs from the sum of the solution to the limit Hele–Shaw problem and the boundary layer type function by quantities of the order $O(\varepsilon)$. The estimates are obtained in Hölder norms. Bibl. 13 titles.
@article{ZNSL_2010_385_a9,
author = {E. V. Frolova},
title = {The order of convergence in the {Stefan} problem with vanishing specific heat},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {206--223},
publisher = {mathdoc},
volume = {385},
year = {2010},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_385_a9/}
}
E. V. Frolova. The order of convergence in the Stefan problem with vanishing specific heat. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Tome 385 (2010), pp. 206-223. http://geodesic.mathdoc.fr/item/ZNSL_2010_385_a9/