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- MakaleYalnız künye2025Scopus SJRQ1An 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.
AtıfScopus2WoS2
İncele - MakaleYalnız künye2022Scopus SJRQ2Lower bounds for blow-up time in a nonlinear parabolic problem with a gradient nonlinearity
Ayazoglu Mashiyev, Rabil; Ekincioglu, Ismail
In this article, we study the blow-up properties of solutions to a parabolic problem with a gradient nonlinearity under homogeneous Dirichlet boundary conditions. By constructing an auxiliary function and by modifying the first order differential inequality, we obtain lower bounds for the blow-up time of solutions in Lk(Ω ) (k> 1 ) norm and conditions which ensure that blow-up cannot occur.
- 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 - DergiJournal of Elliptic and Parabolic Equations
- DergiZeitschrift fur Angewandte Mathematik und Physik