[MS09] The interplay between pure mathematics and mathematical biology

[MS09-05] Immediate smoothing of measure-type population densities in a Keller–Segel system with flux limitation

*Shohei Kohatsu¹ (1. Department of Mathematics, Tokyo University of Science (Japan))

Keywords:

chemotaxis,flux limitation,immediate smoothing

We consider a Keller–Segel system with flux limitation in a bounded domain, for which global existence and boundedness of classical solutions with linear diffusion and regular initial data were considered by Winkler (Math. Nachr.; 2022; 295; 1840–1862). It is shown that under conditions on the strength of diffusion and flux limitation, for any Radon measure initial data the system admits a global solution which immediately becomes smooth and classical, and approaches the given initial data in an appropriate sense.