On an attraction-repulsion chemotaxis model involving logistic source

Year 2024, Early Access, 1 - 14

Ebubekir Akkoyunlu

https://doi.org/10.15672/hujms.1284792

Abstract

This paper is concerned with the attraction-repulsion chemotaxis system involving logistic source: u_{t}=Δu-χ∇⋅(u∇υ)+ξ∇⋅(u∇ω)+f(u), ρυ_{t}=Δυ-α₁υ+β₁u, ρω_{t}=Δω-α₂ω+β₂u under homogeneous Neumann boundary conditions with nonnegative initial data (u₀,υ₀,ω₀)∈ (W^{1,∞}(Ω))³, the parameters χ, ξ, α₁, α₂, β₁, β₂>0, ρ≥0 subject to the non-flux boundary conditions in a bounded domain Ω⊂ℝ^{N}(N≥3) with smooth boundary and f(u)≤au-μu² with f(0)≥0 and a≥0, μ>0 for all u>0. Based on the maximal Sobolev regularity and semigroup technique, it is proved that the system admits a globally bounded classical solution provided that χ+ξ<(μ/2) and there exists a constant β_{∗}>0 is sufficiently small for all β₁, β₂<β_{∗}.

Keywords

Attraction-repulsion, chemotaxis, logistic source, global existence

References

• [1] R. Ayazoglu, Global boundedness of solutions to a quasilinear parabolic-parabolic Keller-Segel system with variable logistic source, J. Math. Anal. Appl. 516 (1), 1- 14, 2022