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Talk abstract:
Spike-Layer Steady States in Diffusion Systems
Michel Rascle, University of Nice
We consider a few models of chemotactism, inspired from the
classical Keller-Segel model, namely
where 
denotes the gradient, u the concentration in predators,
s the concentration in substrate. I will discuss a few
different examples in which the population of predators concentrates
in finite time to a delta-function : aggregation. I
will mainly focus on cartoons, where the diffusion is neglected.
In the unstable case (the + case), aggregation is linked
with a severe pathology in the structure of the underlying system
of conservation laws, which is typically mixed type. However,
I will show how one can mathematically solve the problem, and
even describe such a singular solution after aggregation.
Such solutions seem to be numerically very stable!
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1998-1999
Mathematics in Biology
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