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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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Cite

BibTeXRIS
BibTeX
@misc{geltner2026largetime,
  title = {{Large-time asymptotics for general cross-diffusion systems and novel convex Sobolev inequalities}},
  author = {Noah Geltner and Ansgar Jüngel},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27477},
  eprint = {2609.27477},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27477},
}
RIS
TY  - UNPB
TI  - Large-time asymptotics for general cross-diffusion systems and novel convex Sobolev inequalities
AU  - Noah Geltner
AU  - Ansgar Jüngel
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27477
UR  - https://arxiv.org/abs/2609.27477
AB  - 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.
ER  -