Lower semicontinuous obstacles for the porous medium equation

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorKorte, Riikka
dc.contributor.authorLehtelä, Pekka
dc.contributor.authorSturm, Stefan
dc.contributor.departmentAnalysis
dc.contributor.departmentDepartment of Mathematics and Systems Analysis
dc.contributor.departmentUniversity of Salzburg
dc.date.accessioned2019-05-06T09:03:36Z
dc.date.available2019-05-06T09:03:36Z
dc.date.embargoinfo:eu-repo/date/embargoEnd/2020-12-24
dc.date.issued2019-02-05
dc.description.abstractWe deal with the obstacle problem for the porous medium equation in the slow diffusion regime m>1. Our main interest is to treat fairly irregular obstacles assuming only boundedness and lower semicontinuity. In particular, the considered obstacles are not regular enough to work with the classical notion of variational solutions, and a different approach is needed. We prove the existence of a solution in the sense of the minimal supersolution lying above the obstacle. As a consequence, we can show that non-negative weak supersolutions to the porous medium equation can be approximated by a sequence of supersolutions which are bounded away from zero.en
dc.description.versionPeer revieweden
dc.format.extent14
dc.format.extent1851-1864
dc.format.mimetypeapplication/pdf
dc.identifier.citationKorte , R , Lehtelä , P & Sturm , S 2019 , ' Lower semicontinuous obstacles for the porous medium equation ' , Journal of Differential Equations , vol. 266 , no. 4 , pp. 1851-1864 . https://doi.org/10.1016/j.jde.2018.08.011en
dc.identifier.doi10.1016/j.jde.2018.08.011
dc.identifier.issn0022-0396
dc.identifier.otherPURE UUID: 03da7772-68c2-43d9-9b21-f1da1263b3ae
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/03da7772-68c2-43d9-9b21-f1da1263b3ae
dc.identifier.otherPURE LINK: http://www.scopus.com/inward/record.url?scp=85051108316&partnerID=8YFLogxK
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/32885299/SCI_Korte_Lehtel_Lower_Semicontinuous.PME_obstacle_06_07.pdf
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/37582
dc.identifier.urnURN:NBN:fi:aalto-201905062702
dc.language.isoenen
dc.publisherAcademic Press Inc.
dc.relation.ispartofseriesJournal of Differential Equationsen
dc.relation.ispartofseriesVolume 266, issue 4en
dc.rightsopenAccessen
dc.subject.keywordIrregular obstacles
dc.subject.keywordObstacle problem
dc.subject.keywordPorous medium equation
dc.titleLower semicontinuous obstacles for the porous medium equationen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
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