The nonlocal porous medium equation considered in this paper is a degenerate nonlinear evolution equation involving a space pseudo-differential operator of fractional order. This space-fractional equation admits an explicit, nonnegative, compactly supported weak solution representing a probability density function. In this paper we analyze the link between isotropic transport processes, or random flights, and the nonlocal porous medium equation. In particular, we focus our attention on the interpretation of the weak solution of the nonlinear diffusion equation by means of random flights.

Stochastic models associated to a Nonlocal Porous Medium Equation / De Gregorio, Alessandro. - In: MODERN STOCHASTICS: THEORY AND APPLICATIONS. - ISSN 2351-6054. - 5:4(2018), pp. 457-470. [10.15559/18-VMSTA112]

Stochastic models associated to a Nonlocal Porous Medium Equation

De Gregorio, Alessandro
2018

Abstract

The nonlocal porous medium equation considered in this paper is a degenerate nonlinear evolution equation involving a space pseudo-differential operator of fractional order. This space-fractional equation admits an explicit, nonnegative, compactly supported weak solution representing a probability density function. In this paper we analyze the link between isotropic transport processes, or random flights, and the nonlocal porous medium equation. In particular, we focus our attention on the interpretation of the weak solution of the nonlinear diffusion equation by means of random flights.
2018
anomalous diffusions; finite speed of propagation; fractional gradient; random flights
01 Pubblicazione su rivista::01a Articolo in rivista
Stochastic models associated to a Nonlocal Porous Medium Equation / De Gregorio, Alessandro. - In: MODERN STOCHASTICS: THEORY AND APPLICATIONS. - ISSN 2351-6054. - 5:4(2018), pp. 457-470. [10.15559/18-VMSTA112]
File allegati a questo prodotto
File Dimensione Formato  
DeGregorio_Stochastic-models_2018.pdf

accesso aperto

Tipologia: Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 238.2 kB
Formato Adobe PDF
238.2 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1188497
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact