Stabilization in the Keller–Segel system with signal-dependent sensitivity. Issue 16 (9th December 2020)

• Record Type: Journal Article
• Authors: Black, Tobias; Lankeit, Johannes; Mizukami, Masaaki
• Is Part Of: Applicable analysis. Volume 99:Issue 16(2020)
• Page Start: 2877
• Page End: 2891
• Publication Date: 2020-12-09
• Subjects: J. Shi; Chemotaxis system -- signal-dependent sensitivity -- asymptotic behaviour; 35B40 (primary) -- 35K51 -- 92C17 -- 35Q92 (secondary); Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1585534
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : This paper deals with the Keller–Segel system with signal-dependent sensitivity u t = Δ u − χ ∇ ⋅ ( u S ( v ) ∇ v ), v t = Δ v − v + u, where χ > 0 and S is a given function generalizing the sensitivity S ( s ) = 1 / ( a + s ) k, k >1, a ≥ 0, and shows exponential convergence of global classical solutions under an additional smallness condition for χ > 0 .