preprint

Inserted: 5 jun 2026
Last Updated: 5 jun 2026

Year: 2026

Abstract:

We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a linear pressure law and different mobilities. For arbitrary bounded non-negative initial data, we show that any good approximation scheme, yields existence of global weak solutions. More precisely, we introduce a notion of \textit{admissible approximation sequence} and show that any such sequence admits a subsequence converging to a weak solution of the system. The strategy relies on entropy estimates and the div--curl lemma, in the framework of Young measures.

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