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A. Jüngel:
"Analysis of a cross-diffusion population model";
Keynote Lecture: Workshop "Kinetic modelling for socio-economic and related problems", Vigevano, Italien (invited); 2008-11-27 - 2008-11-29.

In the seventies, Shigesada et al. proposed a generalization of
the Lotka-Volterra differential equations to model spatial
segregation of interacting population species. Segregation comes
from the cross-diffusion terms present in the evolution
equations. Since the diffusion matrix is generally neither
symmetric nor positive definite, an existence theory is far
from being trivial. In this talk, we present recent results for
the population model obtained in collaboration with Li Chen.
The main idea of the analysis is to transform the system to
exponential variables which makes the transformed diffusion matrix
symmetric and positive definite. This also yields a priori
estimates for some entropies functionals. As a consequence, we
specify conditions under which only constant stationary solutions
exist even in the presence of intra-specific competition and
cross-diffusion.

Siehe englischen Abstract.