{"month":"07","article_processing_charge":"No","date_updated":"2023-08-04T10:34:31Z","type":"journal_article","day":"01","department":[{"_id":"JuFi"}],"abstract":[{"text":"We establish sharp criteria for the instantaneous propagation of free boundaries in solutions to the thin-film equation. The criteria are formulated in terms of the initial distribution of mass (as opposed to previous almost-optimal results), reflecting the fact that mass is a locally conserved quantity for the thin-film equation. In the regime of weak slippage, our criteria are at the same time necessary and sufficient. The proof of our upper bounds on free boundary propagation is based on a strategy of “propagation of degeneracy” down to arbitrarily small spatial scales: We combine estimates on the local mass and estimates on energies to show that “degeneracy” on a certain space-time cylinder entails “degeneracy” on a spatially smaller space-time cylinder with the same time horizon. The derivation of our lower bounds on free boundary propagation is based on a combination of a monotone quantity and almost optimal estimates established previously by the second author with a new estimate connecting motion of mass to entropy production.","lang":"eng"}],"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1907.05342","open_access":"1"}],"date_published":"2022-07-01T00:00:00Z","publication_status":"published","issue":"7","publisher":"Taylor & Francis","scopus_import":"1","oa_version":"Preprint","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2023-01-16T10:06:50Z","quality_controlled":"1","title":"Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation","status":"public","external_id":{"arxiv":["1907.05342"],"isi":["000805689800001"]},"publication_identifier":{"eissn":["1532-4133"],"issn":["0360-5302"]},"author":[{"full_name":"De Nitti, Nicola","first_name":"Nicola","last_name":"De Nitti"},{"full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","last_name":"Fischer","orcid":"0000-0002-0479-558X"}],"publication":"Communications in Partial Differential Equations","doi":"10.1080/03605302.2022.2056702","page":"1394-1434","_id":"12304","language":[{"iso":"eng"}],"citation":{"ama":"De Nitti N, Fischer JL. Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation. <i>Communications in Partial Differential Equations</i>. 2022;47(7):1394-1434. doi:<a href=\"https://doi.org/10.1080/03605302.2022.2056702\">10.1080/03605302.2022.2056702</a>","ista":"De Nitti N, Fischer JL. 2022. Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation. Communications in Partial Differential Equations. 47(7), 1394–1434.","apa":"De Nitti, N., &#38; Fischer, J. L. (2022). Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation. <i>Communications in Partial Differential Equations</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.1080/03605302.2022.2056702\">https://doi.org/10.1080/03605302.2022.2056702</a>","chicago":"De Nitti, Nicola, and Julian L Fischer. “Sharp Criteria for the Waiting Time Phenomenon in Solutions to the Thin-Film Equation.” <i>Communications in Partial Differential Equations</i>. Taylor &#38; Francis, 2022. <a href=\"https://doi.org/10.1080/03605302.2022.2056702\">https://doi.org/10.1080/03605302.2022.2056702</a>.","short":"N. De Nitti, J.L. Fischer, Communications in Partial Differential Equations 47 (2022) 1394–1434.","mla":"De Nitti, Nicola, and Julian L. Fischer. “Sharp Criteria for the Waiting Time Phenomenon in Solutions to the Thin-Film Equation.” <i>Communications in Partial Differential Equations</i>, vol. 47, no. 7, Taylor &#38; Francis, 2022, pp. 1394–434, doi:<a href=\"https://doi.org/10.1080/03605302.2022.2056702\">10.1080/03605302.2022.2056702</a>.","ieee":"N. De Nitti and J. L. Fischer, “Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation,” <i>Communications in Partial Differential Equations</i>, vol. 47, no. 7. Taylor &#38; Francis, pp. 1394–1434, 2022."},"article_type":"original","year":"2022","intvolume":"        47","volume":47,"acknowledgement":"N. De Nitti acknowledges the kind hospitality of IST Austria within the framework of the ISTernship Summer Program 2018, during which most of the present article was written. N. DeNitti has received funding by The Austrian Agency for International Cooperation in Education &Research (OeAD-GmbH) via its financial support of the ISTernship Summer Program 2018. N.De Nitti would also like to thank Giuseppe Coclite, Giuseppe Devillanova, Giuseppe Florio, Sebastian Hensel, and Francesco Maddalena for several helpful conversations on topics related to this work.","keyword":["Applied Mathematics","Analysis"],"isi":1}