Abstract
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→+∞ 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.
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This work was partially supported by the Centre National de la Recherche Scientifique through ATP 95939900
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Langlais, M. Large time behavior in a nonlinear age-dependent population dynamics problem with spatial diffusion. J. Math. Biology 26, 319–346 (1988). https://doi.org/10.1007/BF00277394
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DOI: https://doi.org/10.1007/BF00277394