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Special Semester on Quantitative Biology analyzed by Mathematical Methods
Linz, October 1, 2007 - January 27, 2008
Kinetic formulations and the hyperbolic Keller-Segel system

Workshop on Biomechanics and Chemotaxis, Mon, 10 Dec, 2007

Speaker: Benoit Perthame

Abstract

The hyperbolic Keller-Segel system proposed by Dolak and Schmeiser contains quorum sensing and limited random motion of cells. These authors show the qualitative interest of the model, in terms of patterns dynamics, and propose a theory in one dimension. In higher dimensions, the mathematical analysis of this system poses a difficult problem because none of the known methods for scalar conservation laws can be applied to this system.

This talk will review the main methods invented to analyze S. C. L. and we will show that the kinetic formulation provides a possible tool to overcome the difficulties of the hyperbolic Keller-Segel system.

This is a common work with A.-L. Dalibard

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