Lower semicontinuous obstacles for the porous medium equation

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2019-02-05
Major/Subject
Mcode
Degree programme
Language
en
Pages
14
1851-1864
Series
Journal of Differential Equations, Volume 266, issue 4
Abstract
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.
Description
Keywords
Irregular obstacles, Obstacle problem, Porous medium equation
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Citation
Korte , R , Lehtelä , P & Sturm , S 2019 , ' Lower semicontinuous obstacles for the porous medium equation ' , Journal of Differential Equations , vol. 266 , no. 4 , pp. 1851-1864 . https://doi.org/10.1016/j.jde.2018.08.011