Two-dimensional Keller-segel Model : Optimal Critical Mass and Qualitative Properties of the Solutions

  title={Two-dimensional Keller-segel Model : Optimal Critical Mass and Qualitative Properties of the Solutions},
  author={Adrien Blanchet and Jean Dolbeault and Benoit Perthame},
The Keller-Segel system describes the collective motion of cells which 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 solutions and for large initial mass blow-up occurs. In this paper we complete this picture and give a… CONTINUE READING
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