Abstract
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.
Original language | English |
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Pages (from-to) | 425-445 |
Number of pages | 21 |
Journal | Tohoku Mathematical Journal |
Volume | 70 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Sep 2018 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Boundary value problems
- Comparison principle
- Porous medium equation
- Supersolutions
- Very weak solutions
- Weak solutions