3-dimensional physically consistent diffusion in anisotropic media with memory
type: Item
instance of: scholarly article
title: 3-dimensional physically consistent diffusion in anisotropic media with memory
zbMATH Open document ID: 0948.76075
author: Michele Caputo
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2000-11-26T00:00:00Z
review text: Summary: Some data on the flow of fluids exhibit properties which may not be interpreted with the classical theory of propagation of pressure and with the theory of fluids based on the classical Darcy law which states that the flux is proportional to the pressure gradient. In order to obtain a better representation of the flow and of the pressure of fluids, the Darcy law is here modified by introducing a memory formalism operating on the flow as well as on the pressure gradient, which implies a filtering of the pressure gradient without singularities; the properties of the filtering are also described. We also modify the second constitutive equation of diffusion, which relates the density variations of the fluid to its pressure variations, by introducing the rheology of the fluid represented by derivatives of fractional order. Moreover, we are able to consider anisotropic media. We derive a diffusion equation for anisotropic media, and find Green function for a point source.
Mathematics Subject Classification ID: 76R50
Mathematics Subject Classification ID: 76A99
Mathematics Subject Classification ID: 82D15
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 1281959
zbMATH Keywords: modified Darcy law
zbMATH Keywords: anisotropic media
zbMATH Keywords: fluid rheology
zbMATH Keywords: filtering of pressure gradient
zbMATH Keywords: Green function for point source
zbMATH Keywords: memory formalism
zbMATH Keywords: constitutive equation of diffusion
zbMATH Keywords: derivatives of fractional order
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1281959