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.
One contribution of 15 to a theme issue ‘Free boundary problems and related topics’.
- Accepted November 23, 2014.
- © 2015 The Author(s) Published by the Royal Society. All rights reserved.