A Multi-Species Keller-Segel Chemotaxis-Competition Model: Global Existence, Boundedness, and Mass Persistence

This paper investigates the population dynamics of solutions to a parabolic-parabolic-elliptic type of multi-species Keller-Segel chemotaxis system under the Neumann boundary conditions in a smoothly bounded domain. It studies dynamical properties such as $L^\\rho$-bounds, global existence, global boundedness, and combined mass persistence of solutions for the aforementioned system. Under certain specified parameter conditions, the paper shows that the system admits a unique global classical solution that remains uniformly bounded from above. Furthermore, it establishes that the entire population persists at all times; in other words, this study proves that any globally bounded classical solution maintains a positive lower mass bound.