On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density
Articolo
Data di Pubblicazione:
2015
Citazione:
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]
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Porous medium equation; fractional Laplacian; nonlinear diffusion equations; asymptotics of solutions; Barenblatt solution; separable variable solutions
Elenco autori:
G. Grillo, M. Muratori, F. Punzo
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