Asymptotic stabilization for a class of chemotaxis-consumption systems with generalized logistic source. (April 2022)

• Record Type: Journal Article
• Authors: Lyu, Wenbin
• Is Part Of: Nonlinear analysis. Volume 217(2022)
• Publication Date: 2022-04
• Subjects: 35B40 -- 35B35 -- 35K51 -- 35K55 -- 35Q92; Stabilization -- Chemotaxis-consumption -- Generalized logistic source; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112737
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is concerned with a chemotaxis-consumption system u t = ∇ ⋅ ( ∇ u − u S ( x, u, v ) ⋅ ∇ v ) + ρ u − μ u l, v t = Δ v − u v, under no-flux boundary conditions in a smooth bounded domain Ω ⊂ R n ( n ⩾ 1 ), where the chemotactic sensitivity tensor S ∈ C 2 ( Ω ¯ × [ 0, + ∞ ) 2 ; R n × n ) fulfills that there exists some nondecreasing function S 0 on [ 0, + ∞ ) such that | S ( x, u, v ) | ⩽ S 0 ( v ) for all ( x, u, v ) ∈ Ω ¯ × [ 0, + ∞ ) × [ 0, + ∞ ) . We show that for any ρ, μ > 0 and l > 1, any generalized solution of the above system asymptotically approaches to the nontrivial spatially homogeneous steady state ρ μ 1 l − 1, 0 as t → + ∞ .