On two notions of solutions to the obstacle problem for the singular porous medium equation

On two notions of solutions to the obstacle problem for the singular porous medium equation

We show that two different notions of solutions to the obstacle problem for the porous medium equation, a potential theoretic notion and a notion based on a variational inequality, coincide for regular enough compactly supported obstacles.

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Veröffentlicht in:arXiv.org 2024-04
Hauptverfasser: Moring, Kristian, Scheven, Christoph
Format: Artikel
Sprache:eng
Schlagworte:
Barriers
Porous media
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Zusammenfassung:We show that two different notions of solutions to the obstacle problem for the porous medium equation, a potential theoretic notion and a notion based on a variational inequality, coincide for regular enough compactly supported obstacles.
ISSN:2331-8422