Free boundary problems in biology.
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.
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA friedman.158@osu.edu afriedman@mbi.osu.edu.
Avner
A
Friedman
D000818:Animals; D049109:Cell Proliferation / Q000502:physiology*; D003198:Computer Simulation; D004734:Energy Metabolism / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology / Q000503:physiopathology*; D012867:Skin / Q000503:physiopathology*; D014945:Wound Healing / Q000502:physiology*
atherosclerosis; biofilms; cutaneous wounds; granulomas; tumours