Free boundary problems for systems of Stokes equations

Avner  Friedman

doi:10.3934/dcdsb.2016006

Article Contents

2016, Volume 21, Issue 5: 1455-1468. Doi: 10.3934/dcdsb.2016006

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Free boundary problems for systems of Stokes equations

Avner Friedman^1,

1.
The Ohio State University, Department of Mathematics, Columbus, OH 43210

Received: May 2015

Revised: November 2015

Published: July 2016

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Abstract

Recent years have seen a dramatic increase in the number and variety of new mathematical models describing biological processes. Some of these models are formulated as free boundary problems for systems of PDEs. Relevant biological questions give rise to interesting mathematical questions regarding properties of the solutions. In this review we focus on models whose formulation includes Stokes equations. They arise in describing the evolution of tumors, both at the macroscopic and molecular levels, in wound healing of cutaneous wounds, and in biofilms. We state recent results and formulate some open problems.

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Mathematics Subject Classification: Primary: 49J10, 35Q92, 35R35, 76D07, 92C50; Secondary: 35J47, 35K57, 35M30, 35Q30, 35Q92.

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