# Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation

@article{Bailo2021BoundPreservingFS, title={Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation}, author={Rafael Bailo and Jos{\'e} A. Carrillo and Jingwei Hu}, journal={ArXiv}, year={2021}, volume={abs/2110.08186} }

We propose finite-volume schemes for general continuity equations which preserve positivity and global bounds that arise from saturation effects in the mobility function. In the particular case of gradient flows, the schemes dissipate the free energy at the fully discrete level. Moreover, these schemes are generalised to coupled systems of non-linear continuity equations, such as multispecies models in mathematical physics or biology, preserving the bounds and the dissipation of the energy…

## One Citation

Nonlocal cross-interaction systems on graphs: Nonquadratic Finslerian structure and nonlinear mobilities

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We study the evolution of a system of two species with nonlinear mobility and nonlocal interactions on a graph whose vertices are given by an arbitrary, positive measure. To this end, we extend a…

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