2021 UNC Greensboro PDE Conference.
Electron. J. Diff. Eqns., Conference 26 (2022), pp. 139-149.

Title: Wellposedness of Keller-Segel systems in mixed norm spaces

Author: Timothy Robertson (Univ. of Tennessee, Knoxville, USA)
 
Abstract: 
We study the well-posedness of the Cauchy problem for the Keller-Segal system
in the setting of mixed norm spaces. We prove existence of mild solutions 
n scaling invariant spaces and uniqueness in a special case. 
These results allow for existence and uniqueness when the initial data 
has anisotropic properties.
In particular, persistence of anisotropic properties under the evolution 
is demonstrated which could be of biological interest. 

Published August 25, 2022.
Math Subject Classifications: 35A01, 35A02, 92C17.
Key Words: Mixed norm spaces; Keller-Segel model; semigroup methods.