Steady states of a selection-mutation model for an age structured population (original) (raw)

We introduce a selection-mutation model for a density of populations with respect to physiological age and maturation age, where the latter is considered as an evolutionary trait on which the vital rates depend, subject to selection by competition, and to mutation modelled by a convolution-like operator in the birth term. We prove well-posedness of the initial value problem and the existence of non-trivial steady states under suitable hypotheses which give uniqueness when the interaction variable is one-dimensional.