Md. Shahidul Islam
Non-linear Age-time Dependent Population Dynamics
Preprint series: Mathematica Gottingensis

MSC:

47H10 Fixed-point theorems

47H40 Random operators

Abstract: We introduce several non-linear population models, each of
which is an extension of the celebrated Gurtin-MacCamy model [11]. We
give constructive proofs of the existence and uniqueness of a global solution.
More precisely, we show that our model has generally a unique solution in
the future but not in the past. In fact, the model has a unique solution
in the past under certain additional conditions on the birth rate of the
population. Global stability in presence of noise is also considered.
Keywords: Mortality space, Natality space, Gurtin-MacCamy model, Perturbation.