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Large time behavior to a chemotaxis–consumption model with singular sensitivity and logistic source
Author(s) -
Jia Zhe,
Yang Zuodong
Publication year - 2020
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.6971
Subject(s) - bounded function , mathematics , sensitivity (control systems) , chemotaxis , neumann boundary condition , domain (mathematical analysis) , mathematical analysis , boundary (topology) , logistic function , logistic regression , consumption (sociology) , statistics , social science , biochemistry , chemistry , receptor , electronic engineering , sociology , engineering
This paper studies the chemotaxis–consumption model with singular sensitivity and logistic sourceu t = △ u − χ ∇ ·f ( u ) v ∇ v + κ u − μ u 2x ∈ Ω , t > 0 ,v t = ϵ △ v − g ( u ) v , x ∈ Ω , t > 0 ,under homogenous Neumann boundary condition in a smooth bounded domain Ω ⊂ ℝ n ( n ≥ 2 ) , with positive parameters χ , ϵ , μ , and f ( u ) ≃ u α , g ( u ) ≃ u β for α ∈ ℝ and β > 0 . It is shown that the system possesses a global classical solution when α < 1 and 0 < β < 4 n + 2 . Furthermore, the asymptotic behavior of solutions is determined for 0 < α < 1 and 0 < β < α in a two‐dimensional setting, provided a sufficiently large μ .