A fractional porous medium equation

DOI10.1016/J.AIM.2010.07.017zbMATH Open1208.26016arXiv1001.2383OpenAlexW2063595285MaRDI QIDQ616888

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Publication date: 12 January 2011

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Abstract: We develop a theory of existence, uniqueness and regularity for a porous medium equation with fractional diffusion, $fracpartialupartialt+(-Delta{)}^{1/2}(|u{|}^{m-1}u)=0$ 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 $xinmathbb{R}^N$, $t>0$.

Full work available at URL: https://arxiv.org/abs/1001.2383

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