Geodesic
Classical solvability of the radial viscous fingering problem in a Hele--Sha cell with surface tension
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 2, pp. 79-92

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We discuss one-phase radial viscous fingering problem in a Hele–Sha cell with surface tension, which is a nonlinear problem with a free boundary for elliptic equations. Unlike the Stefan problem for heat equation Hele–Sha problem is of hydrodynamic type. In this paper the classical solvability of one-phase Hele–Sha problem with radial geometry is established by applying the same method as for the Stefan problem and justifying the vanishing the coefficient of the time-derivative in a parabolic equation.
Keywords: radial viscous fingering, Hele–Sha problem, classical solution.
Mots-clés : surface tension 
@article{VNGU_2016_16_2_a7,
     author = {Hisasi Tani},
     title = {Classical solvability of the radial viscous fingering problem in a {Hele--Sha} cell with surface tension},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {79--92},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2016_16_2_a7/}
}
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Hisasi Tani. Classical solvability of the radial viscous fingering problem in a Hele--Sha cell with surface tension. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 2, pp. 79-92. http://geodesic.mathdoc.fr/item/VNGU_2016_16_2_a7/