| Abstract: |
| We consider the three-dimensional parabolic-elliptic Keller-Segel model for bacterial chemotaxis. From the work of Brenner et al. in 1999, it is known that this model admits an explicit radial imploding self-similar solution. We prove the nonlinear radial asymptotic stability of this blowup profile. For this, we develop a stability analysis framework that applies to a large class of semilinear parabolic equations. In particular, we outline a robust technique to treat the underlying spectral problems. This is joint work with Birgit Schorkhuber (Innsbruck). |
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