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 innity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at innity, 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.

On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density / G. Grillo, M. Muratori, F. Punzo. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 35:12(2015 Dec), pp. 5927-5962. [10.3934/dcds.2015.35.5927]

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

F. Punzo
2015

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 innity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at innity, 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.
Porous medium equation; fractional Laplacian; nonlinear diffusion equations; asymptotics of solutions; Barenblatt solution; separable variable solutions
Settore MAT/05 - Analisi Matematica
dic-2015
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/331796
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