Decay and asymptotic behavior of solutions of the Keller–Segel system of degenerate and nondegenerate type
Volume 74 / 2006
Banach Center Publications 74 (2006), 161-184
MSC: Primary 35K65; Secondary 35K15, 35K55, 58J35.
DOI: 10.4064/bc74-0-10
Abstract
We classify the global behavior of weak solutions of the Keller–Segel system of degenerate and nondegenerate type. For the stronger degeneracy, the weak solution exists globally in time and has a uniform time decay under some extra conditions. If the degeneracy is weaker, the solution exhibits a finite time blow up if the data is nonnegative. The situation is very similar to the semilinear case. Some additional discussion is also presented.