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.

翻译：本文分析了一类非局部Shigesada-Kawazaki-Teramoto（SKT）交叉扩散系统的有限体积格式。我们证明了该格式解的存在性，推导了解的性质并证明了其收敛性。证明过程依赖于离散熵耗散不等式、离散紧致性论证，以及在离散层面上对所谓对偶方法的新颖改编。最后，通过数值实验，我们研究了系统中非局部性对格式收敛性质、作为局部系统近似时的表现以及扩散不稳定性发展的影响。