# American Institute of Mathematical Sciences

December  2012, 7(4): 691-703. doi: 10.3934/nhm.2012.7.691

## PDE problems arising in mathematical biology

 1 The Ohio State University, Department of Mathematics, Columbus, OH 43210, United States

Received  March 2012 Revised  September 2012 Published  December 2012

This article reviews biological processes that can be modeled by PDEs, it describes mathematical results, and suggests open problems. The first topic deals with tumor growth. This is modeled as a free boundary problem for a coupled system of elliptic, hyperbolic and parabolic equations. Existence theorems, stability of radially symmetric stationary solutions, and symmetry-breaking bifurcation results are stated. Next, a free boundary problem for wound healing is described, again involving a coupled system of PDEs. Other topics include movement of molecules in a neuron, modeled as a system of reaction-hyperbolic equations, and competition for resources, modeled as a system of reaction-diffusion equations.
Citation: Avner Friedman. PDE problems arising in mathematical biology. Networks & Heterogeneous Media, 2012, 7 (4) : 691-703. doi: 10.3934/nhm.2012.7.691
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