id: 06045858
dt: j
an: 06045858
au: Galiano, Gonzalo
ti: Modeling spatial adaptation of populations by a time non-local convection
    cross-diffusion evolution problem.
so: Appl. Math. Comput. 218, No. 8, 4587-4594 (2011).
py: 2011
pu: Elsevier Science Publishing Co. (North-Holland), New York
la: EN
cc: 
ut: population dynamics; finite differences; segregation
ci: 
li: doi:10.1016/j.amc.2011.10.041
ab: Summary: {\it N. Shigesada} et al. [J. Theor. Biol. 79, 83‒99 (1979)]
    presented a system of partial differential equations for modeling
    spatial segregation of interacting species. Apart from competitive
    Lotka-Volterra (reaction) and population pressure (cross-diffusion)
    terms, a convective term modeling the populations attraction to more
    favorable environmental regions is included. We introduce a
    modification of their convective term to take account for the notion of
    spatial adaptation of populations. After describing the model we
    briefly discuss its well-posedness and propose a numerical
    discretization in terms of a mass-preserving time semi-implicit finite
    differences scheme. Finally, we provide the results of two biologically
    inspired numerical experiments showing qualitative differences between
    the original model of Shigesada and the model proposed in this article.
rv: