Interior multiple spikes in the shadow
                  Gierer-Meinhardt system

                             by

            Michal Kowalczyk, University of Utah

         320 JTB, 3:20pm  Monday, November 10, 1997

                          Abstract

 The Gierer-Mienhardt system models biochemical reactions of
 activator-inhibitor type. In such reactions spatial
 patterns of "islands" of high concentration of activator
 (spike layers) within the "sea" of essentially uniformly
 distributed inhibitor are present. The difference between
 the rates of diffusion of the reagents plays crucial role
 in forming of such patterns.

 In this talk I will discuss the existence of stationary
 spike layers in the case when the diffusion of the
 inhibitor is fast (the shadow G-M system). Mathematically
 we will be dealing with a singularly perturbed semilinear
 elliptic problem. In particular the geometric conditions
 for the location of spike layers will be given.

Request for preprints and reprints to kowalcyk@math.utah.edu.
This information can be found at http://www.math.utah.edu/research/