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arXiv · 1801.04244

Porous medium equation with nonlocal pressure

Diana Stan·Félix del Teso·Juan Luis Vázquez
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Abstract

We provide a rather complete description of the results obtained so far on the nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$, which describes a flow through a porous medium driven by a nonlocal pressure. We consider constant parameters $m>1$ and $0 2$, and the asymptotic behavior of solutions when $N=1$. The cases $m = 1$ and $m = 2$ were rather well known.

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Diana Stan, Félix del Teso, Juan Luis Vázquez. 2018-01-12. Porous medium equation with nonlocal pressure. https://arxiv.org/abs/1801.04244

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