Generalized Darcy–Oseen resolvent problem

Dagmar Medková; Mariya Ptashnyk; Werner  Varnhorn

doi:10.1002/mma.3872

Generalized Darcy–Oseen resolvent problem

Dagmar Medková, Mariya Ptashnyk (Lead / Corresponding author), Werner Varnhorn

Mathematics

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Abstract

In this paper we study the well-posedness of a coupled Darcy-Oseen resolvent problem, describing the fluid flow between free fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free-fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy-Oseen resolvent system we consider two auxiliary problem: a mixed Navier-Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations.

Original language	English
Pages (from-to)	1621-1630
Number of pages	10
Journal	Mathematical Methods in the Applied Sciences
Volume	39
Issue number	6
Early online date	29 Feb 2016
DOIs	https://doi.org/10.1002/mma.3872
Publication status	Published - 29 Mar 2016

Keywords

Darcy-Oseen resolven problem
semipermeable membrane
Brinkman-Darcy equations
fluid flow between free fluid domains and porous media
compact perturbations

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10.1002/mma.3872Licence: CC BY

Final Published Version
© 2016 The Authors. Mathematical Methods in the Applied Sciences Published by John Wiley & Sons Ltd. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Final published version, 292 KBLicence: CC BY

Multiscale Modelling and Analysis of Mechanical Properties of Plant Cells and Tissues
Ptashnyk, M. (Investigator)
Engineering and Physical Sciences Research Council
1/01/14 → 31/12/15
Project: Research

Cite this

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title = "Generalized Darcy–Oseen resolvent problem",

abstract = "In this paper we study the well-posedness of a coupled Darcy-Oseen resolvent problem, describing the fluid flow between free fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free-fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy-Oseen resolvent system we consider two auxiliary problem: a mixed Navier-Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations.",

keywords = "Darcy-Oseen resolven problem, semipermeable membrane, Brinkman-Darcy equations, fluid flow between free fluid domains and porous media, compact perturbations",

author = "Dagmar Medkov{\'a} and Mariya Ptashnyk and Werner Varnhorn",

note = "The research of D. M. was supported by RVO: 67985840. The research of M. P. was supported by EPSRC First Grant EP/K036521/1.",

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AU - Medková, Dagmar

AU - Ptashnyk, Mariya

AU - Varnhorn, Werner

N1 - The research of D. M. was supported by RVO: 67985840. The research of M. P. was supported by EPSRC First Grant EP/K036521/1.

PY - 2016/3/29

Y1 - 2016/3/29

N2 - In this paper we study the well-posedness of a coupled Darcy-Oseen resolvent problem, describing the fluid flow between free fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free-fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy-Oseen resolvent system we consider two auxiliary problem: a mixed Navier-Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations.

AB - In this paper we study the well-posedness of a coupled Darcy-Oseen resolvent problem, describing the fluid flow between free fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free-fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy-Oseen resolvent system we consider two auxiliary problem: a mixed Navier-Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations.

KW - Darcy-Oseen resolven problem

KW - semipermeable membrane

KW - Brinkman-Darcy equations

KW - fluid flow between free fluid domains and porous media

KW - compact perturbations

U2 - 10.1002/mma.3872

DO - 10.1002/mma.3872

M3 - Article

SN - 0170-4214

VL - 39

SP - 1621

EP - 1630

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 6

ER -

Generalized Darcy–Oseen resolvent problem

Abstract

Keywords

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Multiscale Modelling and Analysis of Mechanical Properties of Plant Cells and Tissues

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