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Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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  • Johannes Lankeit

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  • Universität Paderborn
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OriginalspracheEnglisch
Seiten (von - bis)1158-1191
Seitenumfang34
FachzeitschriftJournal of differential equations
Jahrgang258
Ausgabenummer4
PublikationsstatusVeröffentlicht - 15 Feb. 2015
Extern publiziertJa

Abstract

We prove existence of global weak solutions to the chemotaxis system. u t=δu-{dot operator}(u;v)+κu-μu 2 v t=δv-v+u under homogeneous Neumann boundary conditions in a smooth bounded convex domain Ω⊂R n, for arbitrarily small values of μ. >. 0.Additionally, we show that in the three-dimensional setting, after some time, these solutions become classical solutions, provided that κ is not too large. In this case, we also consider their large-time behaviour: We prove decay if κ. ≤. 0 and the existence of an absorbing set if κ. >. 0 is sufficiently small.

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Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source. / Lankeit, Johannes.
in: Journal of differential equations, Jahrgang 258, Nr. 4, 15.02.2015, S. 1158-1191.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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KW - Eventual smoothness

KW - Existence

KW - Logistic source

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