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Analysis of a chemotaxis model with indirect signal absorption

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autorschaft

  • Mario Fuest

Externe Organisationen

  • Universität Paderborn
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Details

OriginalspracheEnglisch
Seiten (von - bis)4778-4806
Seitenumfang29
FachzeitschriftJournal of differential equations
Jahrgang267
Ausgabenummer8
PublikationsstatusVeröffentlicht - Okt. 2019
Extern publiziertJa

Abstract

We consider the chemotaxis model {u t=Δu−∇⋅(u∇v),v t=Δv−vw,w t=−δw+u in smooth, bounded domains Ω⊂R n, n∈N, where δ>0 is a given parameter. If either n≤2 or ‖v 0L (Ω) ≤ [Formula presented] we show the existence of a unique global classical solution (u,v,w) and convergence of (u(⋅,t),v(⋅,t),w(⋅,t)) towards a spatially constant equilibrium, as t→∞. The proof of global existence for the case n≤2 relies on a bootstrap procedure. As a starting point we derive a functional inequality for a functional being sublinear in u, which appears to be novel in this context.

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Analysis of a chemotaxis model with indirect signal absorption. / Fuest, Mario.
in: Journal of differential equations, Jahrgang 267, Nr. 8, 10.2019, S. 4778-4806.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Fuest M. Analysis of a chemotaxis model with indirect signal absorption. Journal of differential equations. 2019 Okt;267(8):4778-4806. doi: 10.1016/j.jde.2019.05.015
Fuest, Mario. / Analysis of a chemotaxis model with indirect signal absorption. in: Journal of differential equations. 2019 ; Jahrgang 267, Nr. 8. S. 4778-4806.
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N2 - We consider the chemotaxis model {u t=Δu−∇⋅(u∇v),v t=Δv−vw,w t=−δw+u in smooth, bounded domains Ω⊂R n, n∈N, where δ>0 is a given parameter. If either n≤2 or ‖v 0‖ L ∞(Ω) ≤ [Formula presented] we show the existence of a unique global classical solution (u,v,w) and convergence of (u(⋅,t),v(⋅,t),w(⋅,t)) towards a spatially constant equilibrium, as t→∞. The proof of global existence for the case n≤2 relies on a bootstrap procedure. As a starting point we derive a functional inequality for a functional being sublinear in u, which appears to be novel in this context.

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