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

Wellposedness of Keller-Segel systems in mixed norm spaces

Timothy Robertson

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.
DOI: https://doi.org/10.58997/ejde.conf.26.r1

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Timothy Robertson
Department of Mathematics
University of Tennessee
Knoxville, USA
email: trober41@vols.utk.edu

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