论文标题
Shigesada-kawasaki-teramoto人口系统的一种收敛性结构范围有限体积方案
A convergent structure-preserving finite-volume scheme for the Shigesada-Kawasaki-Teramoto population system
论文作者
论文摘要
shigesada-kawasaki-kawasaki-teramoto-type在一个有界面的域中，提出了和分析的隐性欧拉有限体积方案，用于shigesada-kawasaki-teramoto-type的$ n $ species人群交叉扩散系统。该计划保留了形式的梯度流或熵结构，并保留了人口密度的非神经性。关键思想是以一种适当的方式来考虑一个合适的均值，以使离散的链条规则得以实现，并且熵不平等的离散类似物。证明了有限体积溶液的存在，该方案的收敛性以及对恒定稳态的大渐近液的存在。此外，提出了两个和三个物种的一个和两个空间尺寸的数值实验。结果对于满足某些结构条件的更通用的交叉扩散系统是有效的。
An implicit Euler finite-volume scheme for an $n$-species population cross-diffusion system of Shigesada--Kawasaki--Teramoto-type in a bounded domain with no-flux boundary conditions is proposed and analyzed. The scheme preserves the formal gradient-flow or entropy structure and preserves the nonnegativity of the population densities. The key idea is to consider a suitable mean of the mobilities in such a way that a discrete chain rule is fulfilled and a discrete analog of the entropy inequality holds. The existence of finite-volume solutions, the convergence of the scheme, and the large-time asymptotics to the constant steady state are proven. Furthermore, numerical experiments in one and two space dimensiona for two and three species are presented. The results are valid for a more general class of cross-diffusion systems satisfying some structural conditions.
