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Atelier Mathématiques et biologie 2006–2007

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The two-dimensional Keller-Segel model after blow-up
Christian Schmeiser (univ. Vienne)

16 octobre 2006

The Drift-Diffusion-Poisson system modelling attracting chemotactic interaction between biological cells moving on a two-dimensional surface is considered. Depending on the total cell mass, this model exhibits finite time blow-up of solutions. Several regularizations guaranteeing global existence of smooth solutions will be discussed as well as their global-in-time limits as the regularization parameter vanishes. In the limit, the cell density consists of a regular part and a finite number of point-aggregates. The justification of the limiting procedure uses the theory of Poupaud for the definition of the convective flux for measure valued cell densities. This is joint work with Jean Dolbeault.

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Christian Schmeiser Christian Schmeiser (univ. Vienne)
Professor at the Faculty of Mathematics of the University of Vienna
Program director of the Wolfgang Pauli Institute Vienna
Speaker of the Wissenschaftskolleg "Differential Equations"
Group leader at the Johann Radon Institute for Computational and Applied Mathematics