| Abstract: |
| We show the existence of a unique global minimizer of free energy for all masses that are associated with a nonlinear diffusion type of the Keller-Segel system, but only in cases when the diffusion dominates over the attractive force of the chemo-attractant. We approximate the variational problem in the whole space as a minimization problem posed on bounded balls with large radii. We show that our stationary states have four different properties, they are unique up to translations of the balls^{\prime} center of mass, compactly supported, radially decreasing and smooth within the support of their respective global minimizer. |
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