  The asymptotic stability of the null equilibrium of a linear population model
with two physiological structures formulated as a first-order hyperbolic PDE is
determined by the spectrum of its infinitesimal generator. We propose an
equivalent reformulation of the problem in the space of absolutely continuous
functions in the sense of Carath\'eodory, so that the domain of the
corresponding infinitesimal generator is defined by trivial boundary
conditions. Via bivariate collocation, we discretize the reformulated operator
as a finite-dimensional matrix, which can be used to approximate the spectrum
of the original infinitesimal generator. Finally, we provide test examples
illustrating the converging behavior of the approximated eigenvalues and
eigenfunctions, and its dependence on the regularity of the model coefficients.
