Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : The Keller-Segel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form it is a conservative drift-diffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration. It is known that, in two space dimensions, for small initial mass there is global existence of classical solutions and for large initial mass blow-up occurs. In this note we complete this picture and give an explicit value for the critical mass when the system is set in the whole space.
 
 
OPTIMAL CRITICAL MASS IN THE TWO DIMENSIONAL KELLER-SEGEL MODEL IN R2
DOLBEAULT Jean, PERTHAME BenoƮt
2004-37
29-06-2004
 
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