Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.27477

Authors: Geltner, Noah, Jüngel, Ansgar

Institution: TU Wien

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Austrian Science Fund

Award: Multiphase and multicomponent models

OpenAlex ID: W7214228128

Cites: 1

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Related to: 10