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An attraction‐repulsion chemotaxis system with logistic source
Author(s) -
Zhang Qingshan,
Li Yuxiang
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400311
Subject(s) - bounded function , attraction , homogeneous , chemotaxis , domain (mathematical analysis) , logistic function , logistic regression , mathematics , neumann boundary condition , boundary (topology) , mathematical analysis , combinatorics , statistics , chemistry , philosophy , linguistics , receptor , biochemistry
This paper deals with the attraction‐repulsion chemotaxis system with logistic sourceu t = Δ u − χ ∇ · ( u ∇ v ) + ξ ∇ · ( u ∇ w ) + f ( u ) ,x ∈ Ω , t > 0 ,0 = Δ v + α u − β v ,x ∈ Ω , t > 0 ,0 = Δ w + γ u − δ w ,x ∈ Ω , t > 0 ,under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ R n( n ≥ 1 ) . Under a growth restriction on logistic source and suitable assumptions on the positive parameters χ, ξ, α, β, γ and δ, we show the existence of global bounded classical solutions. The global weak solution is also constructed if the logistic damping effect is rather mild. Furthermore, we obtain the asymptotic behavior of solutions for the logistic source f ( u ) = μ u ( 1 − u ) .