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Title: Porous medium equation and fast diffusion equation as gradient systems (English)
Author: Littig, Samuel
Author: Voigt, Jürgen
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 65
Issue: 4
Year: 2015
Pages: 869-889
Summary lang: English
Category: math
Summary: We show that the Porous Medium Equation and the Fast Diffusion Equation, $\dot u-\Delta u^m=f$, with $m\in (0,\infty )$, can be modeled as a gradient system in the Hilbert space $H^{-1}(\Omega )$, and we obtain existence and uniqueness of solutions in this framework. We deal with bounded and certain unbounded open sets $\Omega \subseteq \mathbb R^n$ and do not require any boundary regularity. Moreover, the approach is used to discuss the asymptotic behaviour and order preservation of solutions. (English)
Keyword: porous medium equation
Keyword: gradient system
Keyword: fast diffusion
Keyword: asymptotic behaviour
Keyword: order preservation
MSC: 34G20
MSC: 35G25
MSC: 47H99
MSC: 47J35
idZBL: Zbl 06537697
idMR: MR3441322
DOI: 10.1007/s10587-015-0214-1
Date available: 2016-01-13T09:01:16Z
Last updated: 2020-07-03
Stable URL:
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