THE EQUIVALENCE OF WEAK AND VERY WEAK SUPERSOLUTIONS TO THE POROUS MEDIUM EQUATION

被引:1
|
作者
Lehtela, Pekka [1 ]
Lukkari, Teemu [1 ]
机构
[1] Aalto Univ, Dept Math, POB 11100, FI-00076 Helsinki, Finland
基金
芬兰科学院;
关键词
Porous medium equation; weak solutions; very weak solutions; supersolutions; comparison principle; boundary value problems; DEGENERATE PARABOLIC EQUATIONS; VISCOSITY SOLUTIONS; DEFINITION;
D O I
10.2748/tmj/1537495355
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove that various notions of supersolutions to the porous medium equation are equivalent under suitable conditions. More spesifically, we consider weak supersolutions, very weak supersolutions, and m-superporous functions defined via a comparison principle. The proofs are based on comparison principles and a Schwarz type alternating method, which are also interesting in their own right. Along the way, we show that Perron solutions with merely continuous boundary values are continuous up to the parabolic boundary of a sufficiently smooth space-time cylinder.
引用
收藏
页码:425 / 445
页数:21
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