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A. Jüngel:
"Cross-diffusion models in biology";
Keynote Lecture: Workshop on Kinetic and Mean-Field Models in the Socio-Economic Sciences, Edinburgh (invited); 2009-07-27 - 2009-07-31.

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 global existence
results for the population model obtained in collaboration with Li
Chen. The main ideas of the analysis are "symmetrizing" variable
transformations and the use of entropy techniques. Related
cross-diffusion systems arising in chemotaxis and tumor growth
modeling are also mentioned.

Siehe englisches Abstract.

Cross-diffusion; population dynamics