Md. Shahidul Islam
Non-linear Age-time Dependent Population Dynamics
Preprint series: Mathematica Gottingensis
47H10 Fixed-point theorems, See also {54H25, 55M20, 58C30}
47H40 Random operators, See also {60H25}
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.