local stability of spike steady states in a simplified gierer-meinhardt system

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ID: 129461
2005
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Ranked #47 of 219 articles by views in icsoft 2006 - 1st international conference on software and data technologies, proceedings

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Abstract
In this paper we study the stability of the single internal spike solution of a simplified Gierer-Meinhardt' system of equations in one space dimension. The linearization around this spike consists of a selfadjoint differential operator plus a non-local term, which is a non-selfadjoint compact integral operator. We find the asymptotic behaviour of the small eigenvalues and we prove stability of the steady state for the parameter $(p,q,r,mu)$ in a four-dimensional region (the same as for the shadow equation, [8]) and for any finite $D$ if $varepsilon$ is sufficiently small. Moreover, there exists an exponentially large $D(varepsilon)$ such that the stability is still valid for $D$ less thatn $D(varepsilon)$. Thus we extend the previous results known only for the case $r=p+1$ or $r=2, 1$ less than $p$ less than $5$.
Reference Key
karadzhov2005electroniclocal Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Georgi E. Karadzhov;David E. Edmunds;Pieter P. N. de Groen
Journal icsoft 2006 - 1st international conference on software and data technologies, proceedings
Year 2005
DOI
DOI not found
URL
http://ejde.math.txstate.edu/Volumes/2005/54/abstr.html
Keywords
mathematics gierer-meinhardt equations

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