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oai:bayburt-rdlopen.rawdatalibrary.net:bayburt/114822026-10-29T19:41:37Zopenairedrivercom_bayburt_10000col_bayburt_10001com_bayburt_10007col_bayburt_10218

Boundedness of solutions to a quasilinear parabolic–parabolic chemotaxis model with variable logistic sourceAyazoglu, RabilAkkoyunlu, EbubekirChemotaxisGlobal boundednessVariable logistic sourceThis paper deals with the higher dimension quasilinear parabolic–parabolic chemotaxis model involving a source term of logistic type ut= ∇ · (ϕ(u) ∇ u) - ∇ · (ψ(u) ∇ υ) + g(x, u) , τυt= Δ υ- 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 ψ, ϕ, g are smooth, positive functions satisfying νsq≤ ψ≤ χsq, ϕ≥ σsp, p, q∈ R, ν, χ, σ> 0 when s≥ s> 1 , g(x, s) ≤ ηsk(x)- μsm(x) for s> 0 , η≥ 0 , μ> 0 constants and g(x, 0) ≥ 0 , x∈ Ω , where k, m are measurable functions with 0≤k-:=essinfx∈Ωk(x)≤k(x)≤m+:=esssupk(x)x∈Ω<+∞, 1<m-:=essinfx∈Ωm(x)≤m(x)≤m+:=esssupm(x)x∈Ω<+∞. We extend the constant exponents k= { 0 , 1 } , m> 1 which in logistic source term g(s) ≤ ηsk- μsm for s> 0 , η≥ 0 , μ> 0 as variable exponents k(·) ≥ 0 , m(·) > 1 with k+< m-. It is proved that if q= m-- 1 (critical case) with μ properly large that μ > μ for some μ> 0 , then there exists a classical solution which is global in time and bounded. Furthermore, if q< m-- 1 , we prove that the classical solutions to the above system are uniformly in-time-bounded without restriction on μ.Birkhauser2022Articlehttps://rdlopen.rawdatalibrary.net/r/bayburt/11482https://doi.org/10.1007/s00033-022-01847-00044-2275enZeitschrift fur Angewandte Mathematik und Physikinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://bayburt-rdlopen.rawdatalibrary.net/tr/items/bayburt/11482