---
_id: '53344'
abstract:
- lang: eng
  text: '<jats:p> A no-flux initial-boundary value problem for the cross-diffusion
    system [Formula: see text] is considered in smoothly bounded domains [Formula:
    see text] with [Formula: see text]. It is shown that whenever [Formula: see text]
    is positive on [Formula: see text] and such that [Formula: see text] for some
    [Formula: see text], for all suitably regular positive initial data a global very
    weak solution, particularly preserving mass in its first component, can be constructed.
    This extends previous results which either concentrate on non-degenerate analogs,
    or are restricted to the special case [Formula: see text]. </jats:p><jats:p> To
    appropriately cope with the considerably stronger cross-degeneracies thus allowed
    through [Formula: see text] when [Formula: see text] is large, in its core part
    the analysis relies on the use of the Moser–Trudinger inequality in controlling
    the respective diffusion rates [Formula: see text] from below. </jats:p>'
author:
- first_name: Michael
  full_name: Winkler, Michael
  last_name: Winkler
citation:
  ama: Winkler M. Application of the Moser–Trudinger inequality in the construction
    of global solutions to a strongly degenerate migration model. <i>Bulletin of Mathematical
    Sciences</i>. 2022;13(02). doi:<a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>
  apa: Winkler, M. (2022). Application of the Moser–Trudinger inequality in the construction
    of global solutions to a strongly degenerate migration model. <i>Bulletin of Mathematical
    Sciences</i>, <i>13</i>(02). <a href="https://doi.org/10.1142/s1664360722500126">https://doi.org/10.1142/s1664360722500126</a>
  bibtex: '@article{Winkler_2022, title={Application of the Moser–Trudinger inequality
    in the construction of global solutions to a strongly degenerate migration model},
    volume={13}, DOI={<a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>},
    number={02}, journal={Bulletin of Mathematical Sciences}, publisher={World Scientific
    Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }'
  chicago: Winkler, Michael. “Application of the Moser–Trudinger Inequality in the
    Construction of Global Solutions to a Strongly Degenerate Migration Model.” <i>Bulletin
    of Mathematical Sciences</i> 13, no. 02 (2022). <a href="https://doi.org/10.1142/s1664360722500126">https://doi.org/10.1142/s1664360722500126</a>.
  ieee: 'M. Winkler, “Application of the Moser–Trudinger inequality in the construction
    of global solutions to a strongly degenerate migration model,” <i>Bulletin of
    Mathematical Sciences</i>, vol. 13, no. 02, 2022, doi: <a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>.'
  mla: Winkler, Michael. “Application of the Moser–Trudinger Inequality in the Construction
    of Global Solutions to a Strongly Degenerate Migration Model.” <i>Bulletin of
    Mathematical Sciences</i>, vol. 13, no. 02, World Scientific Pub Co Pte Ltd, 2022,
    doi:<a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>.
  short: M. Winkler, Bulletin of Mathematical Sciences 13 (2022).
date_created: 2024-04-07T12:55:07Z
date_updated: 2024-04-07T12:55:11Z
doi: 10.1142/s1664360722500126
intvolume: '        13'
issue: '02'
keyword:
- General Mathematics
language:
- iso: eng
publication: Bulletin of Mathematical Sciences
publication_identifier:
  issn:
  - 1664-3607
  - 1664-3615
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Application of the Moser–Trudinger inequality in the construction of global
  solutions to a strongly degenerate migration model
type: journal_article
user_id: '31496'
volume: 13
year: '2022'
...
---
_id: '63284'
abstract:
- lang: eng
  text: '<jats:p> A no-flux initial-boundary value problem for the cross-diffusion
    system [Formula: see text] is considered in smoothly bounded domains [Formula:
    see text] with [Formula: see text]. It is shown that whenever [Formula: see text]
    is positive on [Formula: see text] and such that [Formula: see text] for some
    [Formula: see text], for all suitably regular positive initial data a global very
    weak solution, particularly preserving mass in its first component, can be constructed.
    This extends previous results which either concentrate on non-degenerate analogs,
    or are restricted to the special case [Formula: see text]. </jats:p><jats:p> To
    appropriately cope with the considerably stronger cross-degeneracies thus allowed
    through [Formula: see text] when [Formula: see text] is large, in its core part
    the analysis relies on the use of the Moser–Trudinger inequality in controlling
    the respective diffusion rates [Formula: see text] from below. </jats:p>'
article_number: '2250012'
author:
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Winkler M. Application of the Moser–Trudinger inequality in the construction
    of global solutions to a strongly degenerate migration model. <i>Bulletin of Mathematical
    Sciences</i>. 2022;13(02). doi:<a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>
  apa: Winkler, M. (2022). Application of the Moser–Trudinger inequality in the construction
    of global solutions to a strongly degenerate migration model. <i>Bulletin of Mathematical
    Sciences</i>, <i>13</i>(02), Article 2250012. <a href="https://doi.org/10.1142/s1664360722500126">https://doi.org/10.1142/s1664360722500126</a>
  bibtex: '@article{Winkler_2022, title={Application of the Moser–Trudinger inequality
    in the construction of global solutions to a strongly degenerate migration model},
    volume={13}, DOI={<a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>},
    number={022250012}, journal={Bulletin of Mathematical Sciences}, publisher={World
    Scientific Pub Co Pte Ltd}, author={Winkler, Michael}, year={2022} }'
  chicago: Winkler, Michael. “Application of the Moser–Trudinger Inequality in the
    Construction of Global Solutions to a Strongly Degenerate Migration Model.” <i>Bulletin
    of Mathematical Sciences</i> 13, no. 02 (2022). <a href="https://doi.org/10.1142/s1664360722500126">https://doi.org/10.1142/s1664360722500126</a>.
  ieee: 'M. Winkler, “Application of the Moser–Trudinger inequality in the construction
    of global solutions to a strongly degenerate migration model,” <i>Bulletin of
    Mathematical Sciences</i>, vol. 13, no. 02, Art. no. 2250012, 2022, doi: <a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>.'
  mla: Winkler, Michael. “Application of the Moser–Trudinger Inequality in the Construction
    of Global Solutions to a Strongly Degenerate Migration Model.” <i>Bulletin of
    Mathematical Sciences</i>, vol. 13, no. 02, 2250012, World Scientific Pub Co Pte
    Ltd, 2022, doi:<a href="https://doi.org/10.1142/s1664360722500126">10.1142/s1664360722500126</a>.
  short: M. Winkler, Bulletin of Mathematical Sciences 13 (2022).
date_created: 2025-12-18T19:18:11Z
date_updated: 2025-12-18T20:07:05Z
doi: 10.1142/s1664360722500126
intvolume: '        13'
issue: '02'
language:
- iso: eng
publication: Bulletin of Mathematical Sciences
publication_identifier:
  issn:
  - 1664-3607
  - 1664-3615
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Application of the Moser–Trudinger inequality in the construction of global
  solutions to a strongly degenerate migration model
type: journal_article
user_id: '31496'
volume: 13
year: '2022'
...