Free boundary problems in biology | Zendy

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Free boundary problems in biology

Author(s) -

Avner Friedman

Publication year - 2015

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2014.0368

Subject(s) - mathematical and theoretical biology , uniqueness , boundary (topology) , mathematical model , boundary value problem , free boundary problem , mathematical problem , mathematics , computer science , calculus (dental) , biology , mathematical analysis , bioinformatics , mathematics education , medicine , statistics , dentistry

In this paper, I review several free boundary problems that arise in the mathematical modelling of biological processes. The biological topics are quite diverse: cancer, wound healing, biofilms, granulomas and atherosclerosis. For each of these topics, I describe the biological background and the mathematical model, and then proceed to state mathematical results, including existence and uniqueness theorems, stability and asymptotic limits, and the behaviour of the free boundary. I also suggest, for each of the topics, open mathematical problems.

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