İlgi alanları

• MakaleYalnız künye2026Scopus SJRQ2/r/bayburt/12670
  Boundedness 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.

  AtıfScopus1·WoS1·OpenAlex1

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• MakaleAçık Erişim2026Scopus SJRQ1/r/bayburt/11419
  GLOBAL 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.

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• MakaleAçık Erişim2025Scopus SJRQ2/r/bayburt/12782
  Existence of solutions for anisotropic parabolic Ni-Serrin type equations originated from a capillary phenomena with nonstandard growth nonlinearity

  Ayazoglu, Rabil; Akkoyunlu, Ebubekir; Naghizadeh, Zohreh

  We consider an initial boundary value problem for a class of anisotropic parabolic Ni-Serrin type equations with nonstandard nonlinearity in a bounded smooth domain with homogeneous Dirichlet boundary condition. Because the nonlinear perturbation leads to difficulties (it does not have a definite sign) in obtaining a priori estimates in the energy method, we had to modify the Tartar method significantly. Under suitable assumptions, we obtain the global existence, decay and extinction of solutions.

  AtıfWoS1·OpenAlex1

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• MakaleYalnız künye2025Scopus SJRQ1/r/bayburt/11408
  New 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].

  AtıfScopus2·WoS2·OpenAlex2

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• MakaleYalnız künye2025Scopus SJRQ1/r/bayburt/11164
  An attraction–repulsion chemotaxis with logistic source involving the exponents depending on the spatial variables

  Ayazoglu, Rabil

  We study the quasilinear attraction–repulsion chemotaxis system of parabolic–elliptic type with logistic source involving the exponents depending on the spatial variables: ut=Δu-χ∇·uu+1r-1∇υ+ξ∇·uu+1r-1∇ω+au-bum(x), 0=Δυ-βυ+αu, 0=Δω-δω+γu, where α, β, δ, γ, χ, ξ, b>0, a≥0, r∈R and m:Ω→1,∞ is a measurable function, subject to the homogeneous Neumann boundary conditions in a bounded domain RNN≥1 with smooth boundary. We prove that this system possesses a unique global bounded classical solution, which is an extension of known results, if the repulsion cancels the attraction in the sense that (balance) χα=ξγ with essinfx∈Ωmx>r+N-2+N,1, and if the attraction prevails over the repulsion in the sense that χα>ξγ with essinfx∈Ωmx>maxr+1,1, and if the repulsion prevails over the attraction in the sense that χα<ξγ.

  AtıfScopus2·WoS2

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• MakaleAçık Erişim2024Scopus SJRQ3/r/bayburt/13133
  Global 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.

  AtıfScopus4·OpenAlex4

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• MakaleAçık Erişim2024Scopus SJRQ3/r/bayburt/12954
  Existence and extinction of solutions for parabolic equations with nonstandard growth nonlinearity

  Ayazoglu, Rabil; Alisoy, Gulizar; Akbulut, Sezgin; Aydin, Tuba Agirman

  In this paper, we consider an initial boundary value problem for a class of p(·)-Laplacian parabolic equation with nonstandard nonlinearity in a bounded domain. By using new approach, we obtain the global and decay of existence of the solutions. Moreover, the precise decay estimates of solutions before the occurrence of the extinction are derived.

  AtıfScopus1·WoS1·OpenAlex1

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• MakaleYalnız künye2024Scopus SJRQ3/r/bayburt/12933
  Boundedness 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, ∞).

  İncele
• MakaleYayıncıda açık erişim2024Scopus SJRQ1/r/bayburt/11727
  DYNAMICS IN A PARABOLIC-ELLIPTIC CHEMOTAXIS SYSTEM WITH LOGISTIC SOURCE INVOLVING EXPONENTS DEPENDING ON THE SPATIAL VARIABLES

  Ayazoglu, Rabil; Kadakal, Mahir; Akkoyunlu, Ebubekir

  We consider the parabolic-elliptic chemotaxis system with the exponents depending on the spatial variables logistic source and nonlinear signal production: ut = ∆u−χ∇·(u∇υ)+f(x, u), (x, t) ∈ Ω×(0, T), 0 = ∆υ−υ+uγ in a bounded domain Ω ⊂ RN (N ≥ 1) with smooth boundary, subject to nonnegative initial data and homogeneous Neumann boundary conditions, where χ > 0, γ ≥ 1 and ∂ν∂ denotes the outward normal derivative on ∂Ω. The logistic function f fulfilling f(x, s) ≤ ηs− µsα(x)+1, η ≥ 0, µ > 0 for all s > 0 with f(x, 0) ≥ 0 ∀x ∈ Ω, where α : Ω → [1, ∞) is a measurable function. It is proved that if 1 ≤ α(x) < ∞ for all x ∈ Ω such that essinfx∈Ω α(x) > γ or essinfx∈Ω α(x) = γ with µ > χ, then there exists a nonnegative classical solution (u, υ) that is global-in-time and bounded. In addition, under the particular conditions γ = 1 and f(x, s) = µ(s − sα(x)+1), if µ is sufficiently large, the global bounded solution (u, υ) satisfies ∥u(·, t) − 1∥L∞(Ω) + ∥υ (·, t) − 1∥L∞(Ω) ≤ Ce− Nk+2 t for all t > 0 with k = min n χ42 12o , C > 0. The global-in-time existence and uniform-in-time boundedness of solutions are established under specific parameter conditions, which improves the known results.

  AtıfScopus11·WoS9·OpenAlex11

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• MakaleAçık Erişim2023Scopus SJRQ3/r/bayburt/11828
  Bounds for the blow-up time a class of integro-differential problem of parabolic type with variable reaction term; [Bornes sur le temps d’explosion pour une équation intégro-différentielle de type parabolique avec un terme réactif variable]

  Ayazoglu, Rabil; Akkoyunlu, Ebubekir

  This paper is concerned with the blow-up time of the solutions to an integro-differential problem of parabolic type with variable growth if blow-up occurs. By using the differential inequality technique, we obtain lower bounds for the blow-up time and some global existence results under some conditions to variable exponent of reaction, memory kernel, and initial value.

  AtıfScopus1·WoS1

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