Slow Dynamics of Interior Spikes
in the Shadow Gierer-Meinhardt System


Xinfu Chen
University of Pittsburgh
Department of Mathematics
Pittsburgh, PA 15260

and


Michal Kowalczyk
Carnegie Mellon University
Department of Mathematical Sciences
Pittsburgh, PA 15213



ABSTRACT:

This paper is devoted to the rigorous analysis of the dynamics of single-spike solutions in the shadow Gierer-Meinhardt system. We derive an ODE system 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.

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