# Fast Diffusion leads to partial mass concentration in Keller–Segel type stationary solutions

@article{Carrillo2022FastDL, title={Fast Diffusion leads to partial mass concentration in Keller–Segel type stationary solutions}, author={Jos{\'e} A. Carrillo and Matias G. Delgadino and Rupert L. Frank and Marica Lewin}, journal={Mathematical Models and Methods in Applied Sciences}, year={2022} }

We show that partial mass concentration can happen for stationary solutions of aggregation–diffusion equations with homogeneous attractive kernels in the fast diffusion range. More precisely, we prove that the free energy admits a radial global minimizer in the set of probability measures which may have part of its mass concentrated in a Dirac delta at a given point. In the case of the quartic interaction potential, we find the exact range of the diffusion exponent where concentration occurs in…

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