A model of amplification

A linear model showing behavior of the boundary layer type is developed as a generalization of such a matrix model of Bohl and Lancaster (1993). The governing equations have the form ẋ(t) = Bx(t), x(t) ⩾ 0, t ⩾ 0, where the operator B, being the infinitesimal generator of a semigroup of operators of class C0, depends continuously on a parameter and has discontinuity in the dimension of the null space of B. It is shown that a singular behavior can be detected by a single parameter of imperfection. The analysis depends on a regularization technique for linear operator systems and on a perturbation result of spectral generalized inverse (Drazin). A partial order of the appropriate Banach spaces is another important tool in the investigation.