On singular perturbations and parabolic boundary layers

1968 ◽  
Vol 2 (2) ◽  
pp. 163-172 ◽  
Author(s):  
J. Grasman
Keyword(s):  
Boundary Layers ◽  
Singular Perturbations ◽  
Parabolic Boundary ◽  
Parabolic Boundary Layers

Some comments on a singular elliptic problem associated with a rectangle

1979 ◽  
Vol 83 (3-4) ◽  
pp. 283-296 ◽  
Author(s):  
V. A. Nye
Keyword(s):  
Approximate Solution ◽  
Boundary Layers ◽  
Elliptic Problem ◽  
Boundary Data ◽  
Correction Term ◽  
Parabolic Boundary ◽  
Parabolic Boundary Layers

SynopsisThe construction of the approximate solution within a rectangle of a singular elliptic problem is discussed. It is found that, provided the boundary data satisfy certain continuity conditions at the corners of the rectangle, ordinary boundary layers and parabolic boundary layers only are necessary to describe the solution. A correction term, however, has to be added to the solution if the continuity conditions on the boundary data are not satisfied.

scholarly journals A Survey of Some Topics Related to Differential Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-17
Author(s):  
Denise Huet
Keyword(s):  
Applied Sciences ◽  
Differential Equations ◽  
Boundary Layers ◽  
Singular Perturbations ◽  
Spectral Properties ◽  
Differential Operators ◽  
Inertial Manifolds ◽  
Alphabetical Order ◽  
Linear And Nonlinear ◽  
Young Researchers

This paper is the result of investigations suggested by recent publications and completes the work of Huet, 2010. The topics, which are dealt with, concern some spaces of functions and properties of solutions of linear and nonlinear, stationary and evolution differential equations, namely, existence, spectral properties, resonances, singular perturbations, boundary layers, and inertial manifolds. They are presented in the alphabetical order. The aim of this document and of Huet, 2010, is to be a useful reference for (young) researchers in mathematics and applied sciences.

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