scholarly journals A Variational Singular Perturbation Problem Motivated by Ericksen’s Model for Nematic Liquid Crystals

2021 ◽  
Vol 241 (2) ◽  
pp. 1009-1063
Author(s):  
Dmitry Golovaty ◽  
Itai Shafrir
Keyword(s):  
Liquid Crystals ◽  
Singular Perturbation ◽  
Nematic Liquid Crystals ◽  
Singular Perturbation Problem ◽  
Perturbation Problem

A SINGULAR PERTURBATION PROBLEM IN FRACTURED MEDIA WITH PARALLEL DIFFUSION

1998 ◽  
Vol 08 (04) ◽  
pp. 645-655 ◽  
Author(s):  
J. DAVID LOGAN ◽  
GLENN LEDDER ◽  
MICHELLE REEB HOMP
Keyword(s):  
Boundary Condition ◽  
Singular Perturbation ◽  
Porous Matrix ◽  
Fractured Media ◽  
Singular Perturbation Problem ◽  
Single Fracture ◽  
Direction Parallel ◽  
Flux Boundary Condition ◽  
Perturbation Problem ◽  
Parallel Diffusion

We study differential equations that model contaminant flow in a semi-infinite, fractured, porous medium consisting of a single fracture channel bounded by a porous matrix. Models in the literature usually do not incorporate diffusion in the porous matrix in the direction parallel to the fracture, and therefore they must omit a no-flux boundary condition at the edge, which, in some problems, may be unphysical. Herein we show that the problem usually treated in the literature is the outer problem for a correctly posed singular perturbation problem which includes diffusion in both directions as well as the no-flux boundary condition.

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