The obstacle problem for the porous medium equation
The obstacle problem for the porous medium equation
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DOI：
10.1007/s00208-015-1174-3
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发表时间：
2015-02
影响因子：
1.4
通讯作者：
V. Bögelein;T. Lukkari;Christoph Scheven
中科院分区：
文献类型：
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作者：
V. Bögelein;T. Lukkari;Christoph Scheven
证明了与多孔介质方程有关的障碍问题的存在性结果。对于足够规则的障碍，我们找到了时间导数属于抛物Sobolev空间对偶的连续解。我们还采用弱解的概念，并证明对于更一般的障碍，存在这样的弱解。后一个结果是弱解相对于障碍物的稳定性的结果。
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.