# American Institute of Mathematical Sciences

September  2016, 15(5): 1941-1974. doi: 10.3934/cpaa.2016023

## The Hele-Shaw problem with surface tension in the case of subdiffusion

 1 Institute of Applied Mathematics and Mechanics of NAS of Ukraine, Dobrovolskogo, 1, Slov'iansk, 84100, Ukraine, Ukraine

Received  July 2015 Revised  February 2016 Published  July 2016

In this paper we analyze anomalous diffusion version of the multidimensional Hele-Shaw problem with a nonzero surface tension of a free boundary. We prove the one-valued solvability of this moving boundary problem in the Hölder classes. In the two-dimensional case some numerical solutions are constructed.
Citation: Nataliya Vasylyeva, Vitalii Overko. The Hele-Shaw problem with surface tension in the case of subdiffusion. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1941-1974. doi: 10.3934/cpaa.2016023
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