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Networks and Heterogeneous Media

2012, Volume 7, Issue 4: 691-703. doi: 10.3934/nhm.2012.7.691
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PDE problems arising in mathematical biology

  • 1.
    The Ohio State University, Department of Mathematics, Columbus, OH 43210
  • Received: 01 March 2012 Revised: 01 September 2012

  • Primary: 49J10, 35Q92, 35R35, 92C50; Secondary: 35J47, 35K57, 35L40, 35M30.

  • 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[J]. Networks and Heterogeneous Media, 2012, 7(4): 691-703. doi: 10.3934/nhm.2012.7.691

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  • 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.


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