Advances in Differential Equations

Slow dynamics of interior spikes in the shadow Gierer-Meinhardt system

Xinfu Chen and Michał Kowalczyk

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

This paper is devoted to the rigorous analysis of the dynamics of single-spike solutions in the shadow Gierer-Meinhardt system. We derive a system of ODEs which governs the motion of the spike. Careful analysis of this system shows that the spike moves exponentially slowly towards the point on the boundary that is the closest to the spike.

Article information

Source
Adv. Differential Equations Volume 6, Number 7 (2001), 847-872.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357140566

Mathematical Reviews number (MathSciNet)
MR1828999

Zentralblatt MATH identifier
1032.35025

Subjects
Primary: 35B25: Singular perturbations
Secondary: 35C20: Asymptotic expansions 35K55: Nonlinear parabolic equations 92C15: Developmental biology, pattern formation 92C40: Biochemistry, molecular biology

Citation

Chen, Xinfu; Kowalczyk, Michał. Slow dynamics of interior spikes in the shadow Gierer-Meinhardt system. Adv. Differential Equations 6 (2001), no. 7, 847--872. https://projecteuclid.org/euclid.ade/1357140566.


Export citation