The full Keller-Segel model is well-posed on nonsmooth domains
Horstmann D, Meinlschmidt H, Rehberg J (2018)
Publication Type: Journal article
Publication year: 2018
Journal
Book Volume: 31
Pages Range: 1560-1592
Journal Issue: 4
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.
Authors with CRIS profile
Involved external institutions
Technische Universität Darmstadt
Germany (DE)
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) - Leibniz-Institut im Forschungsverbund Berlin e. V.
Germany (DE)
Universität zu Köln
Germany (DE)
Germany (DE)
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) - Leibniz-Institut im Forschungsverbund Berlin e. V.
Germany (DE)
Universität zu Köln
Germany (DE)
How to cite
APA:
Horstmann, D., Meinlschmidt, H., & Rehberg, J. (2018). The full Keller-Segel model is well-posed on nonsmooth domains. Nonlinearity, 31(4), 1560-1592. https://dx.doi.org/10.1088/1361-6544/aaa2e1
MLA:
Horstmann, D., Hannes Meinlschmidt, and J. Rehberg. "The full Keller-Segel model is well-posed on nonsmooth domains." Nonlinearity 31.4 (2018): 1560-1592.
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