Free boundary problems arising in biology

Avner Friedman

doi:10.3934/dcdsb.2018013

Article Contents

2018, Volume 23, Issue 1: 193-202. Doi: 10.3934/dcdsb.2018013

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Free boundary problems arising in biology

Avner Friedman

Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA

Received: November 30, 2016

Revised: March 31, 2017

Published: November 2017

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Abstract

The present paper describes the general structure of free boundary problems for systems of PDEs modeling biological processes. It then proceeds to review two recent examples of the evolution of a plaque in the artery, and of a granuloma in the lung. Simplified versions of these models are formulated, and rigorous mathematical results and open questions are stated.

Keywords:

Systems of partial differential equations,
wound healing,
atherosclerosis,
cholesterol,
granulomas.

Mathematics Subject Classification: 35Q92, 35R35, 37N25.

Citation:

Full Text(HTML)

Figure 1. A wound $W(t)$ with partially healed tissue $\Omega(t)$

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Figure 2. The plaque occupies the shaded area

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Figure 3. Interplay among cholesterol, macrophages and foam cells

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References

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