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On the Transient Behaviour of Fractional Queues Read chapter Read first chapter

2021 | OriginalPaper | Chapter

Some New Exact Results for Non-linear Space-Fractional Diffusivity Equations

Authors : Arrigo Caserta, Roberto Garra, Ettore Salusti

Published in: Nonlocal and Fractional Operators

Publisher: Springer International Publishing

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Abstract

In this paper we reconsider the classical nonlinear diffusivity equation of real gas in an heterogenous porous medium in light of the recent studies about nonlocal space-fractional generalizations of diffusion models. The obtained equation can be simply linearized into a classical space-fractional diffusion equation, widely studied in the literature. We consider the case of a power-law pressure-dependence of the permeability coefficient. In this case we provide some useful new exact analytical results. In particular, we are able to find a Barenblatt-type solution for a space-fractional Boussinesq equation, arising in this context.

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previous chapter Electromagnetic Waves in Non-local Dielectric Media: Derivation of a Fractional Differential Equation Describing the Wave Dynamics
next chapter A Note on Hermite-Bernoulli Polynomials
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Metadata
Title
Some New Exact Results for Non-linear Space-Fractional Diffusivity Equations
Authors
Arrigo Caserta
Roberto Garra
Ettore Salusti
Copyright Year
2021
Book
Nonlocal and Fractional Operators

Print ISBN: 978-3-030-69235-3

Electronic ISBN: 978-3-030-69236-0

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-69236-0_5

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