Large time behavior in a nonlinear age-dependent population dynamics problem with spatial diffusion.
In this work we analyze the large time behavior in a nonlinear model of population dynamics with age-dependence and spatial diffusion. We show that when t----+ infinity either the solution of our problem goes to 0 or it stabilizes to a nontrivial stationary solution. We give two typical examples where the stationary solutions can be evaluated upon solving very simple partial differential equations. As a by-product of the extinction case we find a necessary condition for a nontrivial periodic solution to exist. Numerical computations not described below show a rapid stabilization.
Langlais
M
M
Université de Bordeaux I, Département de Mathématiques Appliquées, Talence, France.
D000375:Aging; D000818:Animals; D001699:Biometry; D008962:Models, Theoretical; D011157:Population Dynamics; D011336:Probability; D013997:Time Factors