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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.).
- MakaleYalnız künye2026Scopus SJRQ2Boundedness in a parabolic-elliptic chemotaxis system with logistic source involving the exponents depending on the spatial variables and nonlinear signal productions
Ayazoglu, Rabil; Simsek, Ramazan
This paper considers the global boundedness of solutions to the parabolic-elliptic chemotaxis system with a logistic source involving exponents that depend on spatial variables and nonlinear signal production: (Formula presented.) where (Formula presented.), μ, (Formula presented.), and (Formula presented.) is a measurable function, subject to the homogeneous Neumann boundary conditions in a bounded domain (Formula presented.) with smooth boundary. We prove that if either (Formula presented.), (Formula presented.) or (Formula presented.) with (Formula presented.) or (Formula presented.) with (Formula presented.), (Formula presented.) or (Formula presented.), then the above system possesses a unique global bounded classical solution.
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İncele - MakaleYalnız künye2025Scopus SJRQ1New results on the global dynamics for a two-species chemotaxis system with two chemicals and logistic sources
Ayazoglu, Rabil; Ekincioglu, Ismail
This paper deals with the following competitive two-species chemotaxis system with two chemicals with a source term of logistic type ut=Δu−χ1∇⋅(u∇υ)+η1u−μ1u2, υt=Δυ−υ+ω, ωt=Δω−χ2∇⋅(ω∇z)+η2ω−μ2ω2, 0=Δz−z+u, (x,t)∈Ω×(0,T) under homogeneous Neumann boundary conditions [Formula presented] and initial conditions u(x,0)=u0(x), υ(x,0)=υ0(x), ω(x,0)=ω0(x), x∈Ω, in a bounded domain Ω⊂RN (N≥1), where the parameters χ1, μ1, μ2>0 and η1, η2, χ2∈R. It is proved that the corresponding initial-boundary value problem possesses a unique global bounded classical solution if one of the following cases holds: (i)χ2≤0, (ii)χ2>0 as well as μ2 is large enough, which partially improves the results of [25].
AtıfScopus2WoS2OpenAlex2İncele - 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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