Global in time solution to the Keller-Segel model of chemotaxis Academic Article uri icon

abstract

  • We consider the Keller-Segel model of chemotaxis in the radial-symmetric twodimensional case. The blow-up occurs if the size of the initial datum is greater than some threshold. We define the continuation of the solution after its blow-up and provide two ways of regularizing the problem that look quite natural and converge to the solution. Finally, we show that if the size of the initial datum is less than threshold, than all the mass diffuses to the infinity for infinite time whereas, if it is greater than threshold, then all the initial mass concentrates asymptotically in the origin.

publication date

  • January 1, 2004