Existence and uniqueness of a regular solution of the Cauchy-Dirichlet problem for the equation of turbulent filtration
type: Item
instance of: scholarly article
title: Existence and uniqueness of a regular solution of the Cauchy-Dirichlet problem for the equation of turbulent filtration
zbMATH Open document ID: 0957.35067
DOI: 10.1007/BF02680146
author: A. V. Ivanov
author: Willi Jäger
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-12-10T00:00:00Z
review text: In studies of water infiltration through a porous medium in the case of turbulent flows the classical Darcy's law ceases to be true because of large velocities. The flow is described by the equation of turbulent filtration, derived from the continuity equation and from a nonclassical Darcy's law. The aim of this paper is to prove the existence and uniqueness of a regular solution of the Cauchy-Dirichlet problem for turbulent filtration. The term ``regular solution'' means that this solution is Hölder continuous and can be represented as a limit of solutions of some regularized problems. Inner and boundary weighted gradient estimates for the regular solution are established.
reviewed by: Ruxandra Stavre
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 1541252
zbMATH Keywords: turbulent filtration
zbMATH Keywords: regular solution
zbMATH Keywords: existence and uniqueness
zbMATH Keywords: water infiltration through a porous medium
zbMATH Keywords: nonclassical Darcy's law
zbMATH Keywords: inner and boundary weighted gradient estimates
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02680146
OpenAlex ID: W1976671767
description: scientific article; zbMATH DE number 1541252