| Abstract: |
| It is well known that the classical Keller-Segel system has blow-up solutions in two dimensions when the initial mass is greater than the critical mass 8\pi (supercritical case), while has globally bounded solution if the initial mass is less than the critical mass 8\pi (sub-critical case). However the asymptotic behavior of solutions in the sub-critical case still remains unknown. It this talk, I will report a progress made recently. We prove that in the sub-critical case, the radially symmetric solutions will converge to constant equilibrium as time tends to infinity if the domain is a disk. |
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