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Steady states of a selection-mutation model for an age structured population. (English) Zbl 1262.35200

Summary: We introduce a selection-mutation model for an age and age at maturity structured population. The age at maturity is considered an evolutionary trait on which the vital rates depend, subject to selection by competition, and to mutation modelled by a birth term which takes the form of a convolution-like operator. We prove well-posedness of the initial value problem and the existence of non-trivial steady states under suitable hypotheses which yield uniqueness when the interaction variable is one-dimensional.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35F31 Initial-boundary value problems for nonlinear first-order PDEs
92D25 Population dynamics (general)
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