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

Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions. Research Abstract Details 

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Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions. Abstract Text:

Philip K Maini,Juncheng Wei,Matthias Winter,Philip K Maini,Juncheng Wei,Matthias Winter,

We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain Omega subset R(N),A(t)=epsilon(2)DeltaA-A+A(p)/xi(q),x is element of Omega, t>0, tau/Omega/xi(t)=-/Omega/xi+1/xi(s) integral(Omega)A(r)dx, t>0 with the Robin boundary condition epsilon partial differentialA/partial differentialnu+a(A)A=0, x is element of partial differentialOmega, where a(A)>0, the reaction rates (p,q,r,s) satisfy 10, r>0, s>or=0, 1or=0. We rigorously prove the following results on the stability of one-spike solutions: (i) If r=2 and 11 and tau sufficiently small the interior spike is stable. (ii) For N=1 if r=2 and 11 such that for a is element of (a(0),1) and mu=2q/(s+1)(p-1) is element of (1,mu(0)) the near-boundary spike solution is unstable. This instability is not present for the Neumann boundary condition but only arises for the Robin boundary condition. Furthermore, we show that the corresponding eigenvalue is of order O(1) as epsilon-->0.

Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions. Publishing Authors By Initials

PK Maini,J Wei,M Winter,PK Maini,J Wei,M Winter,

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Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions. Journal Published:

PUBLICATION TYPE: Journal Article

Journal: Chaos (Woodbury, N.Y.)

VOLUME: 17

Page Numbers: 037106

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ISSN: 1054-1500

DAY: 1

MONTH: Sep

YEAR: 2007

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

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LANGUAGE: eng

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AFFILIATION: Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, United Kingdom.

Country: United States

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MEDLINETA: Chaos

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