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arXiv · 2609.27477

Large-time asymptotics for general cross-diffusion systems and novel convex Sobolev inequalities

Noah Geltner·Ansgar Jüngel
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Abstract

The exponential decay of weak solutions towards the constant steady state of general cross-diffusion systems in bounded domains with no-flux boundary conditions is investigated. The proof of quantitative decay rates is based on the relative entropy method and involves two parameters: the exponent determining the entropy density and the exponent in the entropy production integral. The key ingredient are novel convex Sobolev inequalities, which extend existing results in the literature to a broad range of values of the two parameters. These inequalities are established using convexity arguments and the Gagliardo-Nirenberg inequality.

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Noah Geltner, Ansgar Jüngel. 2026-09-23. Large-time asymptotics for general cross-diffusion systems and novel convex Sobolev inequalities. https://arxiv.org/abs/2609.27477

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