Sanchez E., Auger Pierre, Poggiale J. C. (2011). Two-time scales in spatially structured models of population dynamics : a semigroup approach. Journal of Mathematical Analysis and Applications, 375 (1), p. 149-165. ISSN 0022-247X.
Titre du document
Two-time scales in spatially structured models of population dynamics : a semigroup approach
Journal of Mathematical Analysis and Applications, 2011,
375 (1), p. 149-165 ISSN 0022-247X
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.
Plan de classement
Sciences fondamentales / Techniques d'analyse et de recherche [020]
