Global boundedness in the higher-dimensional fully parabolic chemotaxis with weak singular sensitivity and logistic source

We consider the following chemotaxis system under homogeneous Neumann boundary conditions in a smooth, open, bounded domain Rⁿ with n 3: equation* cases uₜ = u - (uvᵏ v) + ru - u², & in (0, T ₌₀ₗ), vₜ = v - v + u, & in (0, T ₌₀ₗ), cases equation* where k (0, 1), and, r, , , are positive parameters. In this paper, we demonstrate that for suitably smooth initial data, the problem admits a unique nonnegative classical solution that remains globally bounded in time when is sufficiently large.