For the parabolic-elliptic Keller-Segel system in 2 it has been proved that if the initial mass is less than 8π/χ, a global solution exists, and in case the initial mass is larger than 8π/χ, blow-up happens. The case of several chemotactic species introduces an additional question: What is the analog for the critical mass obtained for the single species system? We find a threshold curve in the two species case that allows us to determine if the system is a blow-up or a global in time solution. No radial symmetry is assumed.
|Number of pages||17|
|Journal||European Journal of Applied Mathematics|
|Publication status||Published - 2013|
- multicomponent Keller-Segel model
- sharp conditions
ASJC Scopus subject areas
- Applied Mathematics