matmessМатематические заметки СВФУMathematical notes of NEFU2411-93262587-876XСеверо-Восточный федеральный университет имени М.К. Аммосова10.25587/SVFU.2018.99.16953matmess-320Research ArticleМАТЕМАТИКАCLASSICAL SOLVABILITY OF THE RADIAL VISCOUS FINGERING PROBLEM IN A HELE–SHAW CELLCLASSICAL SOLVABILITY OF THE RADIAL VISCOUS FINGERING PROBLEM IN A HELE–SHAW CELLTaniA.TaniA.

Atusi Tani

Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan 

Atusi Tani

Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan 

tani@math.keio.ac.jpTaniH.TaniH.

Hisasi Tani

Department of Mechanical Engineering, Texas A&M University, TX 77843-3123, USA

Hisasi Tani

Department of Mechanical Engineering, Texas A&M University, TX 77843-3123, USA

htani0926@tamu.eduKeio UniversityЯпонияKeio UniversityJapanTexas A&M UniversityСоединённые Штаты АмерикиTexas A&M UniversityUnited States20180306202625392114Copyright © Tani A., Tani H., 20262026Tani A., Tani H.Tani A., Tani H.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://matmess.elpub.ru/jour/article/view/320

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. 

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. 

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The authors declare that there are no conflicts of interest present.