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Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions

Abstract:

We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain RN,At=2A−A+,x, t>0, ||t=−||+Ardx, t>0 with the Robin boundary condition +aAA=0, x, where aA>0, the reaction rates (p,q,r,s) satisfy 1

0, r>0, s0, 1<<+, the diffusion constant is chosen such that 1, and the time relaxation constant is such that 0. We rigorously prove the following results on the stability of one-spike solutions: (i) If r=2 and 1

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Publication date:
2007-01-01
URN:
uuid:fe9f9657-3dbe-4d46-a935-c954102b2ead
Local pid:
oai:eprints.maths.ox.ac.uk:661

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