Initial–boundary layer associated with the nonlinear Darcy–Brinkman–Oberbeck–Boussinesq system

Mingwen Fei; Daozhi Han; Xiaoming Wang

doi:10.1016/j.physd.2016.08.002

Initial–boundary layer associated with the nonlinear Darcy–Brinkman–Oberbeck–Boussinesq system

Mingwen Fei
, Daozhi Han
, Xiaoming Wang

Mathematics

Anhui Normal University
Florida State University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, we study the vanishing Darcy number limit of the nonlinear Darcy–Brinkman–Oberbeck–Boussinesq system (DBOB). This singular perturbation problem involves singular structures both in time and in space giving rise to initial layers, boundary layers and initial–boundary layers. We construct an approximate solution to the DBOB system by the method of multiple scale expansions. The convergence with optimal convergence rates in certain Sobolev norms is established rigorously via the energy method.

Original language	English
Pages (from-to)	42-56
Number of pages	15
Journal	Physica D: Nonlinear Phenomena
Volume	338
DOIs	https://doi.org/10.1016/j.physd.2016.08.002
State	Published - Jan 1 2017

Keywords

Boundary layer
Darcy equation
Darcy–Brinkman–Oberbeck–Boussinesq system
Initial layer
Initial–boundary layer
Vanishing Darcy number limit

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10.1016/j.physd.2016.08.002

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title = "Initial–boundary layer associated with the nonlinear Darcy–Brinkman–Oberbeck–Boussinesq system",

abstract = "In this paper, we study the vanishing Darcy number limit of the nonlinear Darcy–Brinkman–Oberbeck–Boussinesq system (DBOB). This singular perturbation problem involves singular structures both in time and in space giving rise to initial layers, boundary layers and initial–boundary layers. We construct an approximate solution to the DBOB system by the method of multiple scale expansions. The convergence with optimal convergence rates in certain Sobolev norms is established rigorously via the energy method.",

keywords = "Boundary layer, Darcy equation, Darcy–Brinkman–Oberbeck–Boussinesq system, Initial layer, Initial–boundary layer, Vanishing Darcy number limit",

author = "Mingwen Fei and Daozhi Han and Xiaoming Wang",

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year = "2017",

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T1 - Initial–boundary layer associated with the nonlinear Darcy–Brinkman–Oberbeck–Boussinesq system

AU - Fei, Mingwen

AU - Han, Daozhi

AU - Wang, Xiaoming

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In this paper, we study the vanishing Darcy number limit of the nonlinear Darcy–Brinkman–Oberbeck–Boussinesq system (DBOB). This singular perturbation problem involves singular structures both in time and in space giving rise to initial layers, boundary layers and initial–boundary layers. We construct an approximate solution to the DBOB system by the method of multiple scale expansions. The convergence with optimal convergence rates in certain Sobolev norms is established rigorously via the energy method.

AB - In this paper, we study the vanishing Darcy number limit of the nonlinear Darcy–Brinkman–Oberbeck–Boussinesq system (DBOB). This singular perturbation problem involves singular structures both in time and in space giving rise to initial layers, boundary layers and initial–boundary layers. We construct an approximate solution to the DBOB system by the method of multiple scale expansions. The convergence with optimal convergence rates in certain Sobolev norms is established rigorously via the energy method.

KW - Boundary layer

KW - Darcy equation

KW - Darcy–Brinkman–Oberbeck–Boussinesq system

KW - Initial layer

KW - Initial–boundary layer

KW - Vanishing Darcy number limit

UR - https://www.scopus.com/pages/publications/84995563978

U2 - 10.1016/j.physd.2016.08.002

DO - 10.1016/j.physd.2016.08.002

M3 - Article

AN - SCOPUS:84995563978

SN - 0167-2789

VL - 338

SP - 42

EP - 56

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

ER -

Initial–boundary layer associated with the nonlinear Darcy–Brinkman–Oberbeck–Boussinesq system

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Keywords

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