论文标题
固定的shigesada-kawasaki-teramoto模型中的全面交叉扩散极限
Full cross-diffusion limit in the stationary Shigesada-Kawasaki-Teramoto model
论文作者
论文摘要
本文研究了shigesada-kawasaki-teramoto模型的共存稳态的渐近行为，因为两种交叉扩散系数往往以相同的速率无穷大。在两个交叉扩散系数中的任何一个倾向于无穷大的情况下，Lou and Ni（1999）得出了几个限制系统，这些系统表征了共存稳态的渐近行为。最近，Kan-On（2020）的正式观察暗示了包括非组织问题在内的限制系统，因为两个交叉扩散系数都以相同的速度无穷大。本文就固定问题提供了严格的证明他的观察。作为证明的关键要素，我们为所有稳态建立了一个统一的$ l^{\ infty} $估计。得益于这一先验估计，我们表明共存稳态的渐近谱可以通过两个限制系统中的任何一个解决方案来表征。
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 (1999) derived a couple of limiting systems, which characterize the asymptotic behavior of coexistence steady states. Recently, a formal observation by Kan-on (2020) 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 $L^{\infty}$ 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 either of two limiting systems.
