The obstacle problem for the porous medium equation

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• 作者：Verena B?gelein ; Teemu Lukkari ; Christoph Scheven
• 关键词：35K65 ; 35K86 ; 35D05 ; 47J20
• 刊名：Mathematische Annalen
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：363
• 期：1-2
• 页码：455-499
• 全文大小：739 KB
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• 作者单位：Verena B?gelein (1)
  Teemu Lukkari (2)
  Christoph Scheven (3)
  
  1. Fachbereich Mathematik, Universit?t Salzburg, Hellbrunner Str. 34, 5020, Salzburg, Austria
  2. Department of Mathematics and Statistics, University of Jyv?skyl?, P.O. Box 35 (MaD), 40014, Jyv?skyl?, Finland
  3. Fakult?t für Mathematik, Universit?t Duisburg-Essen, Thea-Leymann-Str. 9, 45127, Essen, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1807

文摘

We prove existence results for the obstacle problem related to the porous medium equation. For sufficiently regular obstacles, we find continuous solutions whose time derivative belongs to the dual of a parabolic Sobolev space. We also employ the notion of weak solutions and show that for more general obstacles, such a weak solution exists. The latter result is a consequence of a stability property of weak solutions with respect to the obstacle. Mathematics Subject Classification 35K65 35K86 35D05 47J20