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- MakaleAçık Erişim2024Scopus SJRQ3Global attractors in a two-species chemotaxis system with two chemicals and variable logistic sources
Ayazoglu, Rabil; Salmanova, Kamala A.
This paper deals with the higher dimension quasilinear parabolic-parabolic chemotaxis model involving a source term of logistic type (formula presented), subject to the homogeneous Neumann boundary conditions in a Ω ⊂ RN (N ≥ 1) with smooth boundary. It is shown that for the attractionrepulsion case with χ2 ≤ 0, the global boundedness of solutions can be ensured by µ1, µ2 > 0 without any other assumptions, due to the contribution of the logistic sources included in addition to the repulsion mechanism. While for the attraction-attraction case with χ2 > 0, the global boundedness of solutions has to require logistic coefficients µ1, µ2 > 0 such that µ2 properly large.
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İncele - MakaleYalnız künye2022Scopus SJRQ1Global boundedness of solutions to a quasilinear parabolic-parabolic Keller-Segel system with variable logistic source
Ayazoglu, Rabil
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) and [Formula presented] 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.
AtıfScopus10WoS8OpenAlex10
İncele - MakaleAçık Erişim2022Scopus SJRQ1Boundedness of solutions to a quasilinear parabolic–parabolic chemotaxis model with variable logistic source
Ayazoglu, Rabil; Akkoyunlu, Ebubekir
This 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.
AtıfScopus10WoS8OpenAlex10İncele