Operator and integro-differential representations of conditional and unconditional stochastic subsurface flow
type: Item
instance of: scholarly article
title: Operator and integro-differential representations of conditional and unconditional stochastic subsurface flow
zbMATH Open document ID: 0809.76079
DOI: 10.1007/BF01589896
published in: Stochastic Hydrology and Hydraulics
publication date: 1995-04-05T00:00:00Z
review text: We describe an operator representation which avoids the use of Neumann series. It leads to a compact integro-differential form which provides considerable new insight into the nature of the solution. When written in tems of conditional moments, our new representation contains local and nonlocal effective parameters that depend on scale and information. As such, these parameters are not unique material properties but may change as more is learned about the flow system.
Mathematics Subject Classification ID: 76M35
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 86A05
zbMATH DE Number: 687658
zbMATH Keywords: Neumann series
zbMATH Keywords: conditional moments
zbMATH Keywords: effective parameters
author: Shepley Orr
author: Shlomo P. Neuman
MaRDI profile type: Publication
cites work: Stochastic systems
cites work: Q5508799
cites work: Random integral equations
cites work: Q3862820
cites work: Stochastic perturbation analysis of groundwater flow. Spatially variable soils, semi-infinite domains and large fluctuations
cites work: Q5820676
cites work: Functional analysis in modern applied mathematics
cites work: Q3997987
cites work: Q4158998
cites work: Q3997900
cites work: Q3844004
cites work: The structure of isotropic turbulence at very high Reynolds numbers
cites work: Dynamics of Nonlinear Stochastic Systems
cites work: Bounds for effective elastic moduli of disordered materials
cites work: Application of Volterra–Wiener Series for Bounding the Overall Conductivity of Heterogeneous Media. I. General Procedure
cites work: Q3995224
cites work: Q3967411
cites work: Semianalytical methods in stochastic groundwater transport
cites work: Q3853967
cites work: Q3244632
cites work: Random integral equations with applications to life sciences and engineering
cites work: A Perturbation Expansion for Diffusion in a Random Velocity Field
cites work: Stochastic partial differential equations in groundwater hydrology. I: Theory
cites work: A Neumann expansion approach to flow through heterogeneous formations
description: scientific article; zbMATH DE number 687658