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Stabilization in a high‐dimensional chemotaxis system involving arbitrary superlinear degradation
Author(s) -
Zhang Wenji
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7503
Subject(s) - mathematics , bounded function , neumann boundary condition , homogeneous , domain (mathematical analysis) , limit (mathematics) , mathematical analysis , chemotaxis , boundary (topology) , homogeneous function , matrix (chemical analysis) , function (biology) , zero (linguistics) , pure mathematics , combinatorics , materials science , linguistics , philosophy , composite material , evolutionary biology , biology , biochemistry , chemistry , receptor
The chemotaxis‐consumption system with generalized logistic sourceu t = Δ u − ∇ · ( u S ( x , u , v ) · ∇ v ) + λ u − μ u α , x ∈ Ω , t > 0 ,v t = Δ v − u v , x ∈ Ω , t > 0 ,is considered under homogeneous Neumann boundary conditions in a bounded smooth domain Ω ⊂ ℝ n ( n ≥ 1 ) with suitably regular positive initial data. Here λ , μ > 0, α > 1 and S ∈ C 2 ( Ω ¯× [ 0 , ∞ )2 ; ℝ n × n ) is a given matrix‐valued function. We construct globally defined solutions in an appropriately generalized sense and prove that these solutions converge to the spatially homogeneous equilibriumλ μ1 α − 1, 0in the large time limit.