  We analyse the long term behaviour of the measure-valued solutions of a class
of linear renewal equations modelling physiologically structured populations.
The renewal equations that we consider are characterised by a regularisation
property of the kernel. This regularisation property allows to deduce the large
time behaviour of the measure-valued solutions from the asymptotic behaviour of
their absolutely continuous, with respect to the Lebesgue measure, component.
We apply the results to a model of cell growth and fission and to a model of
waning and boosting of immunity. For both models we relate the renewal equation
(RE) to the partial differential equation (PDE) formulation and draw
conclusions about the asymptotic behaviour of the solutions of the PDEs.
