CLASSICAL SOLVABILITY OF THE RADIAL VISCOUS FINGERING PROBLEM IN A HELE–SHAW CELL
https://doi.org/10.25587/SVFU.2018.99.16953
Аннотация
We discuss a single-phase radial viscous fingering problem in a Hele–Shaw cell, which is a nonlinear problem with a free boundary for an elliptic equation. Unlike the Stefan problem for heat equation Hele–Shaw problem is of hydrodynamic type. In this paper a single-phase Hele–Shaw problem in a radial flow geometry admits a unique classical solution by applying the same method as for Stefan problem and justifying the vanishing the coefficient of the derivative with respect to time in a parabolic equation.
Об авторах
A. Tani
Keio University
Япония
Япония
Atusi Tani
Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan
H. Tani
Texas A&M University
Соединённые Штаты Америки
Соединённые Штаты Америки
Hisasi Tani
Department of Mechanical Engineering, Texas A&M University, TX 77843-3123, USA
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Рецензия
Для цитирования:
Tani A., Tani H. CLASSICAL SOLVABILITY OF THE RADIAL VISCOUS FINGERING PROBLEM IN A HELE–SHAW CELL. Математические заметки СВФУ. 2018;25(3):92-114. https://doi.org/10.25587/SVFU.2018.99.16953
For citation:
Tani A., Tani H. CLASSICAL SOLVABILITY OF THE RADIAL VISCOUS FINGERING PROBLEM IN A HELE–SHAW CELL. Mathematical notes of NEFU. 2018;25(3):92-114. (In Russ.) https://doi.org/10.25587/SVFU.2018.99.16953
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