Lower semicontinuous obstacles for the porous medium equation

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

Organisaatiot

  • University of Salzburg

Kuvaus

We deal with the obstacle problem for the porous medium equation in the slow diffusion regime m>1. Our main interest is to treat fairly irregular obstacles assuming only boundedness and lower semicontinuity. In particular, the considered obstacles are not regular enough to work with the classical notion of variational solutions, and a different approach is needed. We prove the existence of a solution in the sense of the minimal supersolution lying above the obstacle. As a consequence, we can show that non-negative weak supersolutions to the porous medium equation can be approximated by a sequence of supersolutions which are bounded away from zero.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut1851-1864
Sivumäärä14
JulkaisuJournal of Differential Equations
Vuosikerta266
Numero4
TilaJulkaistu - 5 helmikuuta 2019
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 30972648