×

zbMATH — the first resource for mathematics

PDE problems arising in mathematical biology. (English) Zbl 1260.49001
Summary: 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.

MSC:
49J10 Existence theories for free problems in two or more independent variables
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35R35 Free boundary problems for PDEs
92C50 Medical applications (general)
35J47 Second-order elliptic systems
35K57 Reaction-diffusion equations
35L40 First-order hyperbolic systems
35M30 Mixed-type systems of PDEs
PDF BibTeX XML Cite
Full Text: DOI