chapter  32
14 Pages

On the Construction of Interior Spike Layer Solutions to a Singularly Perturbed Semilinear Neumann Problem

ByJ. Wei

A singularly perturbed semilinear Neumann problem which models chemotaxis and pattern formation is considered. We establish the existence of interior spike layer solutions for any bounded domain and the location of the interior spike is given. Our construction uses the very properties of the distance function which arises in the estimate of the exponentially small terms.