Boundary Layer Solutions in the Gierer-Meinhardt System

The singularly perturbed Gierer-Meinhardt system has been a prototypical reaction diffusion system for the analysis of localized multi spike solutions. Motivated by recent interest in bulk-surface coupled systems, in this talk we address the structure and linear stability of multi spike solutions in the presence of inhomogeneous boundary conditions. Such inhomogeneities are shown to lead to the formation of both stable symmetric and asymmetric boundary bound spike solutions in one-dimensional domains and analogous solutions in higher dimensions.