Advances in Differential Equations
- Adv. Differential Equations
- Volume 6, Number 7 (2001), 847-872.
Slow dynamics of interior spikes in the shadow Gierer-Meinhardt system
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.
Adv. Differential Equations Volume 6, Number 7 (2001), 847-872.
First available in Project Euclid: 2 January 2013
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35B25: Singular perturbations
Secondary: 35C20: Asymptotic expansions 35K55: Nonlinear parabolic equations 92C15: Developmental biology, pattern formation 92C40: Biochemistry, molecular biology
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