Global Boundedness and Mass Persistence of Solutions to A Chemotaxis-Competition System with Logistic Source

This article examines the population dynamics of solutions such as global existence, global boundedness, and mass persistence, to a parabolic elliptic type of chemotaxis-competition system including logistics kinetics in a smooth bounded domain. Tello and Winkler were the first to investigate the global existence and global boundedness of the system mentioned above. Then Tao and Winkler examined qualitative properties of the given system such as the mass persistence of solutions. This study improves some known results and reveals that under some suitable conditions, there exists a classical solution to the system described above that is globally bounded. In addition, it is shown that the population as a whole is never extinct.