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On single interior spike solutions of the Gierer–Meinhardt system: uniqueness and spectrum estimates

Published online by Cambridge University Press:  01 August 1999

JUNCHENG WEI
JUNCHENG WEI
Affiliation:
Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong
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Abstract

We study the interior spike solutions to a steady state problem of the shadow system of the Gierer–Meinhardt system arising from biological pattern formation. We first show that at a non-degenerate peak point the interior spike solution is locally unique, and then we establish the spectrum estimates of the associated linearized operator. We also prove that the corresponding solution to the shadow system is unstable. Furthermore, the metastability of such solutions is analysed.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 10 , Issue 4 , August 1999 , pp. 353 - 378
Copyright
1999 Cambridge University Press

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