A fractional porous medium equation
de Pablo, Arturo ; Quiros, Fernando ; Rodriguez, Ana ; Vazquez, Juan Luis
arXiv, 1001.2383 / Harvested from arXiv
Text on arXiv
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 $m>m_*=(N-1)/N$, $N\ge1$ and $f\in L^1(\mathbb{R}^N)$. 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 $x\in\mathbb{R}^N$, $t>0$.
Publié le : 2010-01-14
Classification:  Mathematics - Analysis of PDEs,  26A33,  35K55 
@article{1001.2383,
     author = {de Pablo, Arturo and Quiros, Fernando and Rodriguez, Ana and Vazquez, Juan Luis},
     title = {A fractional porous medium equation},
     journal = {arXiv},
     volume = {2010},
     number = {0},
     year = {2010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1001.2383}
}

de Pablo, Arturo; Quiros, Fernando; Rodriguez, Ana; Vazquez, Juan Luis. A fractional porous medium equation. arXiv, Tome 2010 (2010) no. 0, . http://gdmltest.u-ga.fr/item/1001.2383/