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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 Erişim2025Scopus SJRQ2Existence 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.
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İncele - 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*.
- MakaleAçık Erişim2024Scopus SJRQ3Existence 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.
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İncele - MakaleAçık Erişim2023Scopus SJRQ3Bounds 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.
AtıfScopus1WoS1İncele - MakaleYalnız künye2022Extinction 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 .
AtıfScopus2İncele - MakaleAçık Erişim2021Scopus SJRQ2On 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.
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