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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.