The obstacle problem for the porous medium equation

被引：33

作者：

Boegelein, Verena ^{[1
]}

Lukkari, Teemu ^{[2
]}

Scheven, Christoph ^{[3
]}

机构：

[1] Salzburg Univ, Fachbereich Math, A-5020 Salzburg, Austria

[2] Univ Jyvaskyla, Dept Math & Stat, Jyvaskyla 40014, Finland

[3] Univ Duisburg Essen, Fak Math, D-45127 Essen, Germany

来源：

MATHEMATISCHE ANNALEN | 2015年 / 363卷 / 1-2期

关键词：

IRREGULAR OBSTACLES; INEQUALITIES; DEFINITION;

D O I：

10.1007/s00208-015-1174-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：455 / 499

页数：45

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