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Pré-Publication, Document De Travail Année : 2022

Study of a structure preserving finite volume scheme for a nonlocal cross-diffusion system

Résumé

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.
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Dates et versions

hal-03714164 , version 1 (05-07-2022)
hal-03714164 , version 2 (07-07-2022)

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  • HAL Id : hal-03714164 , version 1

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Maxime Herda, Antoine Zurek. Study of a structure preserving finite volume scheme for a nonlocal cross-diffusion system. 2022. ⟨hal-03714164v1⟩
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