The equivalence of weak and very weak supersolutions to the porous medium equation

Pekka Lehtelä, Teemu Lukkari

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)425-445
Number of pages21
JournalTohoku Mathematical Journal
Volume70
Issue number3
DOIs
Publication statusPublished - 1 Sep 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • Boundary value problems
  • Comparison principle
  • Porous medium equation
  • Supersolutions
  • Very weak solutions
  • Weak solutions

Fingerprint Dive into the research topics of 'The equivalence of weak and very weak supersolutions to the porous medium equation'. Together they form a unique fingerprint.

Cite this