Stabilization in a two-species fully parabolic chemotaxis system under small initial conditions

This paper deals with a chemotaxis system with two chemicals in a smoothly bounded domain. It is proven that the solutions of the system are global and bounded as well as exponentially converge to the constant steady-state solutions under small initial conditions. The present work extends the results that in Tao and Winkler (2015) as well as Liu and Dai (2022) to fully parabolic chemotaxis system.