Electron. J. Differential Equations, Vol. 2017 (2017), No. 238, pp. 1-7.

Well-posedness of a porous medium flow with fractional pressure in Sobolev spaces

Xuhuan Zhou, Weiliang Xiao

We prove the existence of a non-negative solution for a linear degenerate diffusion transport equation from which we derive the existence and uniqueness of the solution for the fractional porous medium equation in Sobolev spaces $H^\alpha$ with nonnegative initial data, $\alpha>\frac{d}{2}+1$. We also correct a mistake in our previous paper [14].

Submitted December 22, 2016. Published October 3, 2017.
Math Subject Classifications: 35K55, 35K65, 76S05.
Key Words: Fractional porous medium equation; Sobolev space; degenerate diffusion transport equation.

Show me the PDF file (205 KB), TEX file for this article.

Xuhuan Zhou
Department of Information Technology
Nanjing Forest Police College
210023 Nanjing, China
email: zhouxuhuan@163.com
Weiliang Xiao
School of Applied Mathematics
Nanjing University of Finance and Economics
210023 Nanjing, China
email: xwltc123@163.com

Return to the EJDE web page