  The singularly perturbed Gierer-Meinhardt (GM) system in a bounded
$d$-dimensional domain ($d\geq 2$) is known to exhibit boundary layer (BL)
solutions for a non-zero activator flux. It was previously shown that such BL
solutions can be destabilized by decreasing the activator flux below a
stability threshold. Moreover, numerical simulations previously indicated that
solutions consisting of a boundary layer and interior spike emerge after the
destabilization of a BL solution. In this paper we use the method of matched
asymptotic expansions to investigate the structure and stability of such
"boundary layer spike" (BLS) solutions in the presence of an asymptotically
small activator diffusivity $\varepsilon^2\ll 1$. We find that two types of BLS
solutions, one of which is unconditionally linearly stable and the other
unstable, can be constructed provided that the activator flux is sufficiently
small. In this way we determine that there is an asymptotically large range of
activator flux values for which both the BL solution and one of the BLS
solutions are linearly stable. Formal asymptotic calculations are further
validated by numerically simulating the singularly perturbed GM system.
