Chemotaxis Models with Nonlinear/Porous Medium Diffusion, Consumption, and Logistic source on RN: I. Global Solvability and Boundedness

This series of papers is concerned with the global solvability, boundedness, regularity, and uniqueness of weak solutions to the following parabolic-parabolic chemotaxis system with a logistic source and chemical consumption: equation* cases uₜ = m ( (+u) ^m-1 u) - χ (u v) + u (a - b u), all of these estimates are uniform as 0. In part II, we will study the regularity and uniqueness of weak solutions.