preprint

Inserted: 10 oct 2025
Last Updated: 12 oct 2025

Year: 2025

Abstract:

We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a fast-diffusion law with exponent $0< \alpha\le 1$ and different external potentials. For arbitrary non-negative $L^{1}$ initial data with bounded entropy and a mixing condition we prove the existence of global weak solutions. This extends the recent result of Mészáros and Parker from the linear diffusion ($\alpha=1$) to the fast-diffusion.

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