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• W4284896048 endingPage "126482" @default.
• W4284896048 startingPage "126482" @default.
• W4284896048 abstract "This paper deals with the higher dimension quasilinear parabolic-parabolic Keller-Segel system involving a source term of variable logistic type ut=∇⋅(ϕ(u)∇u)−∇⋅(ψ(u)∇υ)+g(x,u), −Δυ=−υ+u, in (x,t)∈Ω×(0,T), subject to nonnegative initial data and homogeneous Neumann boundary condition, where Ω is a smooth and bounded domain in RN (N≥1) and g∈C1(Ω‾×[0,∞)) function satisfies g(x,s)≤ηsk(x)−μsm(x),s>0 with g(x,0)≥0, x∈Ω and η≥0,μ>0 are constants, k,m are measurable functions with 1<k−:=ess infx∈Ωk(x)≤k(x)≤k+:=esssup k(x)x∈Ω<+∞, 2≤m−:=ess infx∈Ωm(x)≤m(x)≤m+:=esssup m(x)x∈Ω<+∞. Positive functions ψ,ϕ∈C2([0,∞)) satisfy νsq≤ψ≤χsq and ϕ≥σsp with p,q∈R, ν,χ,σ>0 when s≥0. It is proved that if q=m−−1 (critical case) andμ>χ(1−2N(m−−p−1)+),then there exists a classical solution which is global in time and bounded. Moreover, if q∈(k+−1,m−−1), we obtain that there is a classical solution of the above system uniformly in time bounded without any restrictions on m− and μ." @default.
• W4284896048 created "2022-07-09" @default.
• W4284896048 creator A5008967347 @default.
• W4284896048 date "2022-12-01" @default.
• W4284896048 modified "2023-10-11" @default.
• W4284896048 title "Global boundedness of solutions to a quasilinear parabolic-parabolic Keller-Segel system with variable logistic source" @default.
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• W4284896048 doi "https://doi.org/10.1016/j.jmaa.2022.126482" @default.
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