A numerical study of linearized Keller-Segel operator in self-similar variables

Juan F. Campos & Jean Dolbeault
This report is devoted to a numerical study of the Keller-Segel model in self-similar variables. We first parametrize the set of solutions in terms of the mass parameter M ∈ (0, 8π) and consider the asymptotic regimes for M small or M close to 8π. Next we introduce the linearized operator and study its spectrum using various shooting methods: we determine its kernel, the spectrum among radial functions and use a decomposition into spherical harmonics...
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