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- MakaleYalnız künye2026Scopus SJRQ2Global boundedness to a chemotaxis system with modified nonlocal and nonlinear reaction
Akkoyunlu, Ebubekir
This paper deals with the following Neumann initial-boundary value problem (Formula presented.) where (Formula presented.) (Formula presented.) is a bounded domain with smooth boundary, (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.). The initial data satisfy (Formula presented.) where (Formula presented.), (Formula presented.), and (Formula presented.) on (Formula presented.). We rigorously prove that the problem admits a unique global classical solution which is uniformly bounded in time if one of the following conditions holds: (Formula presented.) or (Formula presented.).
- MakaleAçık Erişim2026Scopus SJRQ1GLOBAL BOUNDEDNESS IN A CHEMOTAXIS MODEL WITH SIGNAL-DEPENDENT MOTILITY AND LOGISTIC SOURCE WITH VARIABLE COEFFICIENTS
Ayazoglu, Rabil; Simsek, Ramazan
This paper deals with the following parabolic-parabolic chemotaxis system with growth source { u _ t = ∇· (γ (ε) ∇ u) - ∇· (χ (ε) u ∇v) + η (x) u - μ (x) u ^ α, x ∈Ω, t > 0,; v _ t = Δ v - v + u ^ β, x ∈Ω, t > 0, ]. under homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂ℝ^N (N≥ 2), and the parameters β >0, α >1, and γ ,χ are positive motility functions. Moreover, we assume that η (x) ^ m + α - 1/α - 1/(μ (x) - μ_ *) ^ m/α - 1 is integrable for some m ≥ 1, where η(·) and μ(·) are positive measurable functions satisfying μ(x) > μ_* > 0 for almost every x ∈Ω. Under these conditions, if α > max{2β, 2}, then the system possesses a unique global bounded classical solution.
- MakaleAçık Erişim2025Scopus SJRQ2On an attraction-repulsion chemotaxis model involving logistic source
Akkoyunlu, Ebubekir
This paper is concerned with the attraction-repulsion chemotaxis system involving logistic source: ut = ∆u − χ∇ · (u∇υ) + ξ∇ · (u∇ω) + f(u), ρυt = ∆υ − α1υ + β1u, ρωt = ∆ω − α2ω + β2u under homogeneous Neumann boundary conditions with nonnegative initial data (u0, υ0, ω0) (W1,∞ (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 c RN (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*.
- MakaleYalnız künye2024Scopus SJRQ3Boundedness in a attraction-repulsion chemotaxis system with nonlinear production
Ayazoglu, Rabil
We study the quasilinear attraction-repulsion chemotaxis system of parabolic-elliptic type ut = ∆u−χ∇·(u∇υ)+ξ∇·(u∇ω) with nonlinear production 0 = ∆υ −βυ +αus, 0 = ∆ω −δω +γur, subject to the homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ ℝN (N ≥ 3) with smooth boundary. It is proved that for every α, β, δ, γ, χ, ξ > 0 and s ≥ N2,r > N−2/N s, there exists ξ∗ > 0 such that if ξ > ξ∗ and any sufficiently regular initial datum u0(x) ≥ 0, then the model has a unique global classical solution (u, υ, ω), which is bounded in Ω × (0, ∞).
- 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.
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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
