Stochastic models associated to a Nonlocal Porous Medium Equation
Volume 5, Issue 4 (2018), pp. 457–470
Pub. online: 19 September 2018
Type: Research Article
Open Access
Open Access
Received
24 April 2018
24 April 2018
Revised
19 July 2018
19 July 2018
Accepted
24 August 2018
24 August 2018
Published
19 September 2018
19 September 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.
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