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.

Department(s)

Mathematics and Statistics

Comments

This work was completed during the first author's visit to the Florida State University. He is grateful for the hospitality of the math department. First author was supported by NSFC grant 11301005 , CSC grant 201508340024 and AHNSF grant 1608085MA13 . Third author was supported by NSF grant DMS-1312701.

Keywords and Phrases

Physics; Approximate solution; Boussinesq system; Darcy equations; Darcy number; Initial layer; Method of multiple scale; Optimal convergence; Singular perturbation problems; Boundary layers; Boundary layer; Darcy-Brinkman-Oberbeck-Boussinesq system; Initial layer; Initial-boundary layer; Vanishing Darcy number limit

International Standard Serial Number (ISSN)

0167-2789

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2017 Elsevier, All rights reserved.

Publication Date

01 Jan 2017

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