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