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December  2003, 2(4): 521-537. doi: 10.3934/cpaa.2003.2.521

On the dynamics of a mixed parabolic-gradient system

J. K. Krottje 1,

1. 

CWI, P.O. Box 94079, 1090 GB Amsterdam, Netherlands

Received  December 2002 Revised  June 2003 Published  October 2003

In the current paper the dynamics of a mixed parabolic-gradient system is examined. The system, which is a coupled system of parabolic equations and gradient equations, acts as a first model for the outgrowth of axons in a developing nervous system. For modeling considerations it is relevant to know the influence of the parameters in the system and the source profiles in the parabolic equations on the dynamics. These subjects are discussed together with an approximation which uses the quasi-steady-state solutions of the parabolic equations instead of the parabolic equations themselves.
Some of the findings are demonstrated by numerical simulations.
Keywords: computational neurobiology., mixed systems, Parabolic equations, gradient equations.
Mathematics Subject Classification: Primary: 70K99, 35K55, 65M99, 92C2.
Citation: J. K. Krottje. On the dynamics of a mixed parabolic-gradient system. Communications on Pure & Applied Analysis, 2003, 2 (4) : 521-537. doi: 10.3934/cpaa.2003.2.521
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