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

Nataliya  Vasylyeva; Vitalii  Overko

doi:10.3934/cpaa.2016023

Article Contents

2016, Volume 15, Issue 5: 1941-1974. Doi: 10.3934/cpaa.2016023

This issue Previous Article Distributionally chaotic families of operators on Fréchet spaces Next Article

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

Nataliya Vasylyeva^1, and
Vitalii Overko^1,

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

Received: June 30, 2015

Revised: January 31, 2016

Published: August 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 35R35, 35C15; Secondary: 35B65, 35R11.

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