[{"publication":"Bulletin of Mathematical Sciences","type":"journal_article","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>"}],"status":"public","_id":"53344","user_id":"31496","keyword":["General Mathematics"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1664-3607","1664-3615"]},"publication_status":"published","issue":"02","year":"2022","intvolume":"        13","citation":{"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>","short":"M. Winkler, Bulletin of Mathematical Sciences 13 (2022).","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>.","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} }","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>.","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>.","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>"},"date_updated":"2024-04-07T12:55:11Z","publisher":"World Scientific Pub Co Pte Ltd","volume":13,"author":[{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"date_created":"2024-04-07T12:55:07Z","title":"Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model","doi":"10.1142/s1664360722500126"},{"_id":"63284","user_id":"31496","article_number":"2250012","language":[{"iso":"eng"}],"publication":"Bulletin of Mathematical Sciences","type":"journal_article","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>"}],"status":"public","date_updated":"2025-12-18T20:07:05Z","publisher":"World Scientific Pub Co Pte Ltd","volume":13,"date_created":"2025-12-18T19:18:11Z","author":[{"first_name":"Michael","last_name":"Winkler","id":"31496","full_name":"Winkler, Michael"}],"title":"Application of the Moser–Trudinger inequality in the construction of global solutions to a strongly degenerate migration model","doi":"10.1142/s1664360722500126","publication_identifier":{"issn":["1664-3607","1664-3615"]},"publication_status":"published","issue":"02","year":"2022","intvolume":"        13","citation":{"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>","short":"M. Winkler, Bulletin of Mathematical Sciences 13 (2022).","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>.","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} }","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>.","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>.","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>"}}]