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The dynamics and pinning of a spike for a reaction-diffusion system

Abstract:

The motion of a one-spike solution to a simplified form of the Gierer--Meinhardt activator-inhibitor model is studied in both a one-dimensional and a two-dimensional 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 one-dimensional case, we derive a differential equation for the trajectory of the spike in the limit $\epsilon \rightarrow 0$,...

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Publication date:
2002-01-01
UUID:
uuid:cf1e1971-4f32-4de3-b6df-b51b11013a62
Local pid:
oai:eprints.maths.ox.ac.uk:394
Deposit date:
2011-05-19

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