e-journal

Global small-data solutions of a two-dimensional chemotaxis system with rotational flux terms

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under no-flux boundary conditions in a bounded planar convex domain with smooth boundary, where f and S are given parameter functions on Ω × [0,∞)2 with values in [0,∞) and R2×2, respectively, which are assumed to satisfy certain regularity assumptions and growth restrictions. Systems of type (
), in the special case S ≡“1 0 0 1 ”
reducing to a version of the standard Keller–Segel system with signal consumption, have recently been proposed as a model for swimming bacteria near a surface, with the sensitivity tensor then given by S ≡“ 0 1 −1 0”, reflecting rotational chemotactic motion. It is shown that for any choice of suitably regular initial data (u0, v0) fulfilling a smallness condition on the norm of v0 in L∞(Ω), the corresponding initial-boundary value problem associated with (
) possesses a globally defined classical solution which is bounded.This result is achieved through the derivation of a series of a priori estimates involving an interpolation inequality of Gagliardo–Nirenberg type which appears to be new in this context. It is next proved that all corresponding solutions approach a spatially homogeneous
steady state of the form (u, v) ≡ (μ, κ) in the large time limit, with μ := fΩu0 and some κ ≥ 0. A mild additional assumption on the positivity of f is shown to guarantee that κ = 0. Finally, numerical solutions are presented which suggest the occurrence of wave-like solution behavior.

Keywords: Keller–Segel model; rotational flux; global existence; asymptotic behavior

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Ketersediaan

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Informasi Detail

Judul Seri

Mathematical Models and Methods in Applied Sciences

No. Panggil

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Penerbit

: World Scientific., 2015

Deskripsi Fisik

Mathematical Models and Methods in Applied Sciences Vol. 25, No. 4 (2015) 721–746

Bahasa

English

ISBN/ISSN

DOI: 10.1142/S021820

Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

Vol. 25, No. 4 (2015) 721–746

Subjek

KESEHATAN

Info Detail Spesifik

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Pernyataan Tanggungjawab

Wati/Agus

Versi lain/terkait

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