A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Johannes Lankeit

Externe Organisationen

  • Universität Paderborn
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Details

OriginalspracheEnglisch
Seiten (von - bis)394-404
Seitenumfang11
FachzeitschriftMathematical Methods in the Applied Sciences
Jahrgang39
Ausgabenummer3
Frühes Online-Datum16 Apr. 2015
PublikationsstatusVeröffentlicht - 1 Feb. 2016
Extern publiziertJa

Abstract

We consider the parabolic chemotaxis model ut=Δu-χ∇·uv∇vvt=Δv-v+u in a smooth, bounded, convex two-dimensional domain and show global existence and boundedness of solutions for χ∈(0,χ0) for some χ0>1, thereby proving that the value χ = 1 is not critical in this regard. Our main tool is consideration of the energy functional Fa,b(u,v)=∫Ωulnu-a∫Ωulnv+b∫Ω∇v2 for a > 0, b≥0, where using nonzero values of b appears to be new in this context.

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A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity. / Lankeit, Johannes.
in: Mathematical Methods in the Applied Sciences, Jahrgang 39, Nr. 3, 01.02.2016, S. 394-404.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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