@article{Jiao2025, 
author = {Zhan Jiao},
title = {Boundedness in a quasilinear attraction–repulsion chemotaxis system with variable logistic source},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {19867-19877},
keywords = {chemotaxis, attraction–repulsion, nonlinear diffusion, variable logistic source, global boundedness},
url = {https://www.sciopen.com/article/10.3934/math.2025886},
doi = {10.3934/math.2025886},
abstract = {This paper deals with a quasilinear attraction–repulsion chemotaxis system with a source term of variable logistic type        u    t    =  ∇  ⋅  (  ϕ  (  u  )  ∇  u  )  −  ∇  ⋅  (  ψ  (  u  )  ∇  v  )  +  ∇  ⋅  (  φ  (  u  )  ∇  w  )  +  g  (  u  ),        τ    1        v    t    =  Δ  v  −  v  +  u,    −  Δ  w  =  −  w  +  u in a smooth bounded domain    Ω  ⊂            R        n   (   n  ≥  1), and endowed with nonnegative initial data and homogeneous Neumann boundary conditions. Moreover, the logistic source verifies    g  (  x  ,  s  )  ≤  η      s          k      (      x      )        −  μ      s          m      (      x      )      ,    s  >  0 with    g  (  x  ,  0  )  ≥  0,    x  ∈  Ω, where    η  ≥  0,    μ  >  0 are constants,    k  ,  m are measurable functions fulfilling    0  ≤      k    −    :=            e      s      s            inf              x      ∈      Ω        k  (  x  )  ≤  k  (  x  )  ≤      k    +    :=            e      s      s            sup              x      ∈      Ω        k  (  x  )  <  +  ∞ and    1  <      m    −    :=            e      s      s            inf              x      ∈      Ω        m  (  x  )  ≤  m  (  x  )  ≤      m    +    :=            e      s      s            sup              x      ∈      Ω        m  (  x  )  <  +  ∞, as well as    ϕ  ,  ψ, and    φ are regular functions satisfying        c    1        s    p    ≤  ϕ  (  s  ),    ψ  (  s  )  ≤      c    2        s    q  , and              c      _        3        s    l    ≤  φ  (  s  )  ≤      c    3        s    l   with    p  ,  q  ,  l  ∈      R  ,        c    1    ,      c    2    ,            c      _        3    ,      c    3    >  0 and    s  ≥      s    0    >  1. We show that when    q  =      m          −        −  1 and    l  ≤      m          −        −  1, there exists        μ    ∗    >  0 such that if    μ  >      μ    ∗  , then the corresponding initial-boundary value problem possesses a unique globally bounded classical solution. Moreover, the same conclusion holds true provided that    q  <      m          −        −  1 and    l  ≤      m          −        −  1 for any    μ  >  0.}
}