{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,29]],"date-time":"2025-11-29T14:19:35Z","timestamp":1764425975193,"version":"3.46.0"},"reference-count":12,"publisher":"IOP Publishing","issue":"11","license":[{"start":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T00:00:00Z","timestamp":1634083200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T00:00:00Z","timestamp":1634083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"crossref","award":["715734"],"award-info":[{"award-number":["715734"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2021,11,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We study the convergence of the weak solution of the porous medium equation with a type of Robin boundary conditions, by tuning a parameter either to zero or to infinity. The convergence is in the strong sense, with respect to the\n                    <jats:italic>L<\/jats:italic>\n                    <jats:sup>2<\/jats:sup>\n                    -norm, and the limiting function solves the same equation with Neumann (resp. Dirichlet) boundary conditions when the parameter is taken to zero (resp. infinity). Our approach is to consider an underlying microscopic dynamics whose space\u2013time evolution of the density is ruled by the solution of those equations and from this, we derive sufficiently strong energy estimates which are the keystone to the proof of our convergence result.\n                  <\/jats:p>","DOI":"10.1088\/1361-6544\/ac2a16","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T17:09:00Z","timestamp":1634749740000},"page":"7872-7915","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Energy estimates and convergence of weak solutions of the porous medium equation"],"prefix":"10.1088","volume":"34","author":[{"given":"R","family":"De Paula","sequence":"first","affiliation":[]},{"given":"P","family":"Gon\u00e7alves","sequence":"additional","affiliation":[]},{"given":"A","family":"Neumann","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2021,10,13]]},"reference":[{"key":"nonac2a16bib1","doi-asserted-by":"publisher","first-page":"748","DOI":"10.1007\/s10955-020-02550-y","type":"journal-article","article-title":"Hydrodynamics of porous medium model with slow reservoirs","volume":"179","author":"Bonorino","year":"2020","journal-title":"J. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2021-05-18","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-09-24","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-10-13","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}