Ward, M. J. and McInerney, D. and Houston, P. and Gavaghan, D. J. and Maini, P. K. (2002) The dynamics and pinning of a spike for a reactiondiffusion system. SIAM Journal of Applied Maths, 62 (4). pp. 12971328.

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Abstract
The motion of a onespike solution to a simplified form of the GiererMeinhardt activatorinhibitor model is studied in both a onedimensional and a twodimensional domain. The pinning effect on the spike motion associated with the presence of spatially varying coefficients in the differential operator, referred to as precursor gradients, is studied in detail. In the onedimensional case, we derive a differential equation for the trajectory of the spike in the limit , where is the activator diffusivity. A similar differential equation is derived for the twodimensional problem in the limit for which and , where is the inhibitor diffusivity. A numerical finiteelement method is presented to track the motion of the spike for the full problem in both one and two dimensions. Finally, the numerical results for the spike motion are compared with corresponding asymptotic results for various examples.
Item Type:  Article 

Uncontrolled Keywords:  spike; Green's function; finiteelement method; pinning; GiererMeinhardt 
Subjects:  A  C > Biology and other natural sciences 
Research Groups:  Centre for Mathematical Biology 
ID Code:  394 
Deposited By:  Philip Maini 
Deposited On:  20 Nov 2006 
Last Modified:  29 May 2015 18:21 
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