Advances in Differential Equations

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

Xinfu Chen and Michał Kowalczyk

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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

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

First available in Project Euclid: 2 January 2013

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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.

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