# American Institute of Mathematical Sciences

November  2012, 17(8): 2691-2712. doi: 10.3934/dcdsb.2012.17.2691

## A three dimensional model of wound healing: Analysis and computation

 1 Department of Mathematics and Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210, United States, United States 2 Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556

Received  March 2011 Revised  May 2011 Published  July 2012

This paper is concerned with a three-dimensional model of wound healing. The boundary of the wound is a free boundary, and the region surrounding it is viewed as a partially healed tissue, satisfying a viscoelastic constitutive law for the velocity v. In the partially healed region the densities of several types of cells and the concentrations of several chemical species satisfy a coupled system of parabolic equations, whereas the tissue density satisfies a hyperbolic equation. The parabolic equations include advection by the velocity v and chemotaxis/haptotaxis terms. We prove existence and uniqueness of a smooth solution of the free boundary problem, for some time interval $0\leq t\leq T$, $T>0$. We also simulate the model equations to demonstrate the difference in the healing rate between normal wounds and chronic (or ischemic) wounds.
Citation: Avner Friedman, Bei Hu, Chuan Xue. A three dimensional model of wound healing: Analysis and computation. Discrete & Continuous Dynamical Systems - B, 2012, 17 (8) : 2691-2712. doi: 10.3934/dcdsb.2012.17.2691
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