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We study the existence of global boundedness solutions to the fully parabolic chemotaxis systems with logistic sources, ru- u², under nonlinear Neumann boundary conditions, u = |u|ᵖ where p >1 in smooth bounded domain Rⁿ with n 2. A recent study by Le (2023) has shown that the logistic sources can ensure that solutions are global and bounded when n =2 with p < 32 and n=3 with p <75. In this paper, we extend the previous findings by demonstrating the existence of global bounded solutions when p< 32 in any spatial dimension n 2.
Minh Le (Mon,) studied this question.