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We consider a parabolic-elliptic type of Keller-Segel equations withgeneralized diffusion and logistic source under homogeneous Neumann-Neumannboundary conditions. We construct bounded weak solutions globally in time in anunbalanced optimal transport framework, provided that the magnitude of thechemotactic sensitivity can be restricted depending on parameters. In the caseof subquadratic degradation of the logistic source, we quantify the chemotacticsensitivity, in particular, in terms of the power of degradation and thepointwise bound of the initial density.

Bounded weak solutions for Keller-Segel equations with generalized  diffusion and logistic source via an unbalanced Optimal Transport splitting  scheme