Abstract
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.
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Acknowledgments
We acknowledge the warm hospitality of the Institut Mittag-Leffler in the Fall 2013 during the program “Evolutionary problems”, during which we initiated our collaboration on this paper.
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Bögelein, V., Lukkari, T. & Scheven, C. The obstacle problem for the porous medium equation. Math. Ann. 363, 455–499 (2015). https://doi.org/10.1007/s00208-015-1174-3
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DOI: https://doi.org/10.1007/s00208-015-1174-3