İlgi alanları

• MakaleYalnız künye2026Scopus SJRQ2/r/bayburt/12777
  Global 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.).

  İncele
• 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

  İncele
• MakaleAçık Erişim2025Scopus SJRQ2/r/bayburt/12689
  On 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*.

  İncele
• MakaleAçık Erişim2024/r/bayburt/12999
  Global Existence in a Predator-Prey Model with Nonlinear Indirect Chemotaxis Mechanism

  Akkoyunlu, Ebubekir

  One of the fundamental processes in ecology is the interaction between predator and prey. Predator-prey interactions refer to the relative changes in population density of two species as they share the same environment and one species preys on the other. There are many studies global existence or blow-up of solutions on the predator-prey model. Our this paper related to the predator-prey model with nonlinear indirect chemotaxis mechanism under homogeneous Neumann boundary conditions. We establish the global existence and boundedness of classical solutions of our problem by using parabolic regularity theory. Namely, firstly we show that and boundedness in for some, then we obtain the-bound of and by using Alikakos-Moser iteration. Thus, it is proved that the model has a unique global classical solution under suitable conditions on the parameters in a smooth bounded domain.

  AtıfScopus1·OpenAlex1

  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

  İncele
• 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

  İncele
• MakaleYalnız künye2022/r/bayburt/13501
  Extinction properties of solutions for a parabolic equation with a parametric variable exponent nonlinearity

  Ayazoglu Mashiyev, Rabil; Akkoyunlu, Ebubekir

  In this paper, we study a class of p(·)-Laplace equation including nonstandard growth nonlinearity in a bounded smooth domain with homogeneous Dirichlet boundary condition. We establish the conditions of non-extinction and extinction are studied of global weak solutions in finite time for any initial data u0 . Moreover, we show the global existence results for N ≥ 1 with constant p for any initial data u0 .

  AtıfScopus2

  İncele
• MakaleAçık Erişim2022Scopus SJRQ2/r/bayburt/13190
  Existence and multiplicity of solutions for p(.)-Kirchhoff-type equations

  Ayazoğlu, Rabil; Akbulut, Sezgin; Akkoyunlu, Ebubekir

  This paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for p(.) - Kirchhoff-type equation (Formula Presented). Using the mountain pass theorem, fountain theorem, dual fountain theorem and the theory of the variable exponent Sobolev spaces, under appropriate assumptions on f and M, we obtain results on existence and multiplicity of solutions

  AtıfScopus9·WoS9·OpenAlex9

  İncele
• MakaleAçık Erişim2022Scopus SJRQ1/r/bayburt/11482
  Boundedness 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.

  AtıfScopus10·WoS8·OpenAlex10

  İncele
• MakaleAçık Erişim2021Scopus SJRQ2/r/bayburt/13451
  On global existence and bounds for the blow-up time in a semilinear heat equation involving parametric variable sources

  Ayazoglu, Rabil; Akkoyunlu, Ebubekir; Aydin, Tuba Agirman

  This paper is concerned with the blow-up of the solutions to a semilinear heat equation with a reaction given by parametric variable sources. Some conditions to parameters and exponents of sources are given to obtain lower–upper bounds for the time of blow-up and some global existence results.

  AtıfScopus3·WoS2·OpenAlex2

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