Perturbation of spectral inverses applied to a boundary layer phenomenon arising in chemical networks (Q1210388)

A linear model of the form \(x'=B(a,b)x\), \(x\geq 0\), \(t\geq 0\), which has boundary layer type behavior is developed. The matrix \(B\) has a rank discontinuity at the origin of \((a,b)\) parameter space. The analysis depends on a regularization technique for linear systems and a perturbation result for spectral (group) inverses. The theoretical results are applied to a compartmental model arising in the study of chemical networks.