Stochastic models associated to a Nonlocal Porous Medium Equation
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 d...
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| Format: | Article |
| Language: | English |
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VTeX
2018-09-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://www.vmsta.org/doi/10.15559/18-VMSTA112 |
| Summary: | 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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| ISSN: | 2351-6046 2351-6054 |