Yazar "Ayazoglu, Rabil A." seçeneğine göre listele

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    Boundedness in a attraction-repulsion chemotaxis system with nonlinear production
    (Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2024) Ayazoglu, Rabil A.
    We study the quasilinear attraction-repulsion chemotaxis system of parabolic-elliptic type ut = ?u???·(u??)+??·(u??) with nonlinear production 0 = ?? ??? +?us, 0 = ?? ??? +?ur, subject to the homogeneous Neumann boundary conditions in a bounded domain ? ? ?N (N ? 3) with smooth boundary. It is proved that for every ?, ?, ?, ?, ?, ? > 0 and s ? N2,r > N?2/N s, there exists ?? > 0 such that if ? > ?? and any sufficiently regular initial datum u0(x) ? 0, then the model has a unique global classical solution (u, ?, ?), which is bounded in ? × (0, ?). © 2024, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.
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    Global attractors in a two-species chemotaxis system with two chemicals and variable logistic sources
    (Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2024) Ayazoglu, Rabil A.; 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 ? ? RN (N ? 1) with smooth boundary. It is shown that for the attractionrepulsion case with ?2 ? 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 ?2 > 0, the global boundedness of solutions has to require logistic coefficients µ1, µ2 > 0 such that µ2 properly large. © 2024, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.