%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Sanchez, E.
%A Auger, Pierre
%A Poggiale, J. C.
%T Two-time scales in spatially structured models of population dynamics : a semigroup approach
%D 2011
%L fdi:010053395
%G ENG
%J Journal of Mathematical Analysis and Applications
%@ 0022-247X
%K Aggregation of variables ; Two-time scales ; Spatially structured ; population dynamics ; Reaction-diffusion equations
%M ISI:000284293600013
%N 1
%P 149-165
%R 10.1016/j.jmaa.2010.08.014
%U https://www.documentation.ird.fr/hor/fdi:010053395
%> https://www.documentation.ird.fr/intranet/publi/2011/03/010053395.pdf
%V 375
%W Horizon (IRD)
%X The aim of this work is to provide a unified approach to the treatment of a class of spatially structured population dynamics models whose evolution processes occur at two different time scales. In the setting of the C-0-semigroup theory, we will consider a general formulation of some semilinear evolution problems defined on a Banach space in which the two-time scales are represented by a parameter epsilon > 0 small enough, that mathematically gives rise to a singular perturbation problem. Applying the so-called aggregation of variables method, a simplified model called the aggregated model is constructed. A nontrivial mathematical task consists of comparing the asymptotic behaviour of solutions to both problems when epsilon -> 0(+), under the assumption that the aggregated model has a compact attractor. Applications of the method to a class of two-time reaction-diffusion models of spatially structured population dynamics and to models with discrete spatial structure are given.
%$ 020