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- W4301969892 abstract "We develop a theory of existence, uniqueness and regularity for a porous medium equation with fractional diffusion, $frac{partial u}{partial t} + (-Delta)^{1/2} (|u|^{m-1}u)=0$ in $mathbb{R}^N$, with $m>m_*=(N-1)/N$, $Nge1$ and $fin L^1(mathbb{R}^N)$. An $L^1$-contraction semigroup is constructed and the continuous dependence on data and exponent is established. Nonnegative solutions are proved to be continuous and strictly positive for all $xinmathbb{R}^N$, $t>0$." @default.
- W4301969892 created "2022-10-06" @default.
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- W4301969892 date "2010-01-14" @default.
- W4301969892 modified "2023-10-09" @default.
- W4301969892 title "A fractional porous medium equation" @default.
- W4301969892 doi "https://doi.org/10.48550/arxiv.1001.2383" @default.
- W4301969892 hasPublicationYear "2010" @default.
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