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Boundedness in a two‐dimensional attraction–repulsion system with nonlinear diffusion
Author(s) -
Li Xie
Publication year - 2016
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.3477
Subject(s) - attraction , mathematics , dimension (graph theory) , diffusion , nonlinear system , space (punctuation) , chemotaxis , mathematical analysis , pure mathematics , mathematical physics , physics , computer science , thermodynamics , quantum mechanics , chemistry , operating system , receptor , biochemistry , philosophy , linguistics
This paper is devoted to the attraction–repulsion chemotaxis system with nonlinear diffusion:u t = ∇ · ( D ( u ) ∇ u ) − χ ∇ · ( u ∇ v ) + ζ ∇ · ( u ∇ w ) + uf ( u ) , x ∈ Ω , t > 0 ,v t = Δv − α 1 v + β 1 u , x ∈ Ω , t > 0 ,w t = Δw − α 2 w + β 2 u , x ∈ Ω , t > 0 ,where χ > 0, ζ > 0, α i >0, β i >0 ( i = 1,2) and f ( s )≤ κ − μ s τ . In two‐space dimension, we prove the global existence and uniform boundedness of the classical solution to this model for any μ > 0. Copyright © 2015 John Wiley & Sons, Ltd.