Full cross-diffusion limit in the stationary Shigesada-Kawasaki-Teramoto model

Abstract This paper studies the asymptotic behavior of coexistence steady-states Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at same rate. In case when either one two tends infinity, Lou and Ni [18] derived a couple limiting systems, which characterize steady-states. Recently, formal observation by Kan-on [10] implied existence system including nonstationary problem gives rigorous proof his far stationary problem. As key ingredient proof, we establish uniform L ? estimate for all Thanks this priori estimate, show that profile can be characterized solution system.