Well-posedness of a porous medium flow with fractional pressure in Sobolev spaces
The nonnegative solution for a linear degenerate diffusion transport eqution is proved. As a result, we show the existence and uniqueness of the solution for the fractional porous medium equation in Sobolev spaces \(H^\alpha\) with nonnegative initial data, \(\alpha>\frac d2+1\). Besides, we corr...
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| Veröffentlicht in: | arXiv.org 2016-12 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | The nonnegative solution for a linear degenerate diffusion transport eqution is proved. As a result, we show the existence and uniqueness of the solution for the fractional porous medium equation in Sobolev spaces \(H^\alpha\) with nonnegative initial data, \(\alpha>\frac d2+1\). Besides, we correct a mistake in our previous paper \cite{zhou01}. |
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| ISSN: | 2331-8422 |