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

## 抄録

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

本文言語 English Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire https://doi.org/10.1016/j.anihpc.2021.02.006 Accepted/In press - 2021

• 分析
• 数理物理学
• 応用数学

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