Global solvability to a singular chemotaxis-consumption model with fast and slow diffusion and logistic source (Q2120327)

A model of chemotaxis with the consumption of chemoattractant term \(-u^rv\), a nonlinear diffusion, the logarithmic sensitivity function and the logistic reaction term is studied in bounded domains of \(\mathbb R^N\), under no-flux boundary conditions. Assuming \(r<\frac{4}{N+2}\), the existence of global-in-time, locally bounded weak solution is shown for the initial data of arbitrary size.