Analysis of a population model with strong cross-diffusion in
unbounded domains
M. Dreher
Abstract.
We study a parabolic population model in the full space and prove the
global in time existence of a weak solution. This model consists of
two strongly coupled diffusion equations describing the population
densities of two competing species. The system features intrinsic
growth, inter- and intra-specific competition of the species, as well
as diffusion, cross-diffusion and self-diffusion, and drift terms
related to varying environment quality. The cross-diffusion terms can
be large, making the system non-parabolic for large initial data. The
method of our proof is a combination of a time semi-discretization, a
special entropy symmetrizing the system, and compactness arguments.
Royal Soc. Edinburgh Proc. A
138
(2008), 769-786.
A preprint version of the paper is available here:
pdf.
