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

Carrillo, J. A.; Delgadino, M. G.; Frank, Rupert L. und Lewin, M. (2022): Fast Diffusion leads to partial mass concentration in Keller-Segel type stationary solutions. In: Mathematical Models & Methods in Applied Sciences, Bd. 32, Nr. 4: S. 831-850

Abstract

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 space dimensions N >= 6. We then provide numerical computations which suggest the occurrence of mass concentration in all dimensions N >= 3, for homogeneous interaction potentials with higher power.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Analysis, Mathematische Physik und Numerik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 0218-2025
• Sprache: Englisch