We consider the one-phase problem on radial viscous fingering structures in a Hele–Shaw cell with surface tension. This problem is a nonlinear free-boundary problem for elliptic equations. Unlike the Stefan problem for the heat equation, we deal with a problem of hydrodynamic type. We establish the classical solvability of the one-phase Hele–Shaw problem with radial geometry by using the same method as that used for the Stefan problem and justifying the vanishing coefficient of the time-derivative in the parabolic equation.
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Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 16, No. 2, 2016, pp. 79-92.
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Tani, H. Classical Solvability of the Radial Viscous Fingering Problem in a Hele–Shaw Cell with Surface Tension. J Math Sci 228, 449–462 (2018). https://doi.org/10.1007/s10958-017-3634-7
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DOI: https://doi.org/10.1007/s10958-017-3634-7