Universität zu Köln

Horstmann, D., Meinlschmidt, H. and Rehberg, J. (2018). The full Keller-Segel model is well-posed on nonsmooth domains. Nonlinearity, 31 (4). S. 1560 - 1593. BRISTOL: IOP PUBLISHING LTD. ISSN 1361-6544

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Abstract

In this paper we prove that the full Keller-Segel system, a quasilinear strongly coupled reaction-crossdiffusion system of four parabolic equations, is well-posed in the sense that it always admits an unique local-in-time solution in an adequate function space, provided that the initial values are suitably regular. The proof is done via an abstract solution theorem for nonlocal quasilinear equations by Amann and is carried out for general source terms. It is fundamentally based on recent nontrivial elliptic and parabolic regularity results which hold true even on rather general nonsmooth spatial domains. For space dimensions 2 and 3, this enables us to work in a nonsmooth setting which is not available in classical parabolic systems theory. Apparently, there exists no comparable existence result for the full Keller-Segel system up to now. Due to the large class of possibly nonsmooth domains admitted, we also obtain new results for the ` standard' Keller-Segel system consisting of only two equations as a special case.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Horstmann, D. UNSPECIFIED UNSPECIFIED UNSPECIFIED Meinlschmidt, H. UNSPECIFIED UNSPECIFIED UNSPECIFIED Rehberg, J. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-190516
DOI:	10.1088/1361-6544/aaa2e1
Journal or Publication Title:	Nonlinearity
Volume:	31
Number:	4
Page Range:	S. 1560 - 1593
Date:	2018
Publisher:	IOP PUBLISHING LTD
Place of Publication:	BRISTOL
ISSN:	1361-6544
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MIXED BOUNDARY-CONDITIONS; PARABOLIC EVOLUTION-EQUATIONS; BLOW-UP; CHEMOTAXIS MODEL; GLOBAL EXISTENCE; MAXIMAL REGULARITY; SOBOLEV REGULARITY; PATTERN-FORMATION; SYSTEM; NEUMANN Multiple languages Mathematics, Applied; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/19051