Geodesic
Local stability of spike steady states in a simplified Gierer-Meinhardt system
Electronic Journal of Differential Equations, Tome 2005 (2005).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $r=p+1$ or .
Classification : 35B25, 35K60
Keywords: spike solution, singular perturbations, reaction-diffusion equations, Gierer-Meinhardt equations 
@article{EJDE_2005__2005__a229,
     author = {Karadzhov, Georgi E. and Edmunds, David and de Groen, Pieter},
     title = {Local stability of spike steady states in a simplified {Gierer-Meinhardt} system},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2005},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a229/}
}
TY  - JOUR
AU  - Karadzhov, Georgi E.
AU  - Edmunds, David
AU  - de Groen, Pieter
TI  - Local stability of spike steady states in a simplified Gierer-Meinhardt system
JO  - Electronic Journal of Differential Equations
PY  - 2005
VL  - 2005
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a229/
LA  - en
ID  - EJDE_2005__2005__a229
ER  - 
%0 Journal Article
%A Karadzhov, Georgi E.
%A Edmunds, David
%A de Groen, Pieter
%T Local stability of spike steady states in a simplified Gierer-Meinhardt system
%J Electronic Journal of Differential Equations
%D 2005
%V 2005
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a229/
%G en
%F EJDE_2005__2005__a229
Karadzhov, Georgi E.; Edmunds, David; de Groen, Pieter. Local stability of spike steady states in a simplified Gierer-Meinhardt system. Electronic Journal of Differential Equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a229/