论文标题
非本地交叉扩散系统的熵耗散有限体积方案的研究
Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system
论文作者
论文摘要
在本文中，我们分析了Shigesada-Kawazaki-Feramoto（SKT）跨扩散系统的非本地版本的有限体积方案。我们证明了该方案的解决方案的存在，得出了解决方案的定性特性，并证明了其收敛性。这些证明依赖于离散的熵散失不平等，离散的紧凑性参数以及在离散级别的新型二元方法的新颖适应。最后，借助数值实验，我们研究了系统中非局部性的影响：对于该方案的收敛属性，作为局部系统的近似值以及扩散不稳定性的发展。
In this paper we analyse a finite volume scheme for a nonlocal version of the Shigesada-Kawazaki-Teramoto (SKT) cross-diffusion system. We prove the existence of solutions to the scheme, derive qualitative properties of the solutions and prove its convergence. The proofs rely on a discrete entropy-dissipation inequality, discrete compactness arguments, and on the novel adaptation of the so-called duality method at the discrete level. Finally, thanks to numerical experiments, we investigate the influence of the nonlocality in the system: on convergence properties of the scheme, as an approximation of the local system and on the development of diffusive instabilities.
