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arXiv · 2107.11289

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

Georg Heinze·Jan-Frederik Pietschmann·Markus Schmidtchen
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Abstract

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 recently introduced $2$-Wasserstein-type quasi-metric on generalized graphs, which is based on an upwind-interpolation, to the case of two-species systems, concave, nonlinear mobilities, and $p\ne 2$. We provide a rigorous interpretation of the interaction system as a gradient flow in the Finslerian setting, arising from the new quasi-metric.

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Georg Heinze, Jan-Frederik Pietschmann, Markus Schmidtchen. 2021-07-23. Nonlocal cross-interaction systems on graphs: Nonquadratic Finslerian structure and nonlinear mobilities. https://arxiv.org/abs/2107.11289

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