Asymptotic Behavior of Solutions of Two-Species Chemotaxis System with Strong Competition

This paper is concerned with a chemotaxis-competition system modeling the spatiotemporal evolution of two species that proliferate and compete according to Lotka–Volterra-type kinetics. We study the asymptotic behavior of solutions in the case of strong competition and show that they spatially segregate as the competition rate tends to infinity. Moreover, using a blow-up method, we obtain the uniform Hölder continuity of the solutions.