On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

Gabriele Grillo; Matteo Muratori; Fabio Punzo

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arXiv · 1403.5293

On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

Gabriele Grillo·Matteo Muratori·Fabio Punzo

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Abstract

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.

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Gabriele Grillo, Matteo Muratori, Fabio Punzo. 2014-03-20. On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density. https://arxiv.org/abs/1403.5293

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