Corner Boundary Layer in Boundary Value Problems for Singularly Perturbed Parabolic Equations with Nonlinearities

2019 ◽  
Vol 59 (1) ◽  
pp. 96-111 ◽  
Author(s):  
A. I. Denisov ◽  
I. V. Denisov
Keyword(s):  
Boundary Layer ◽  
Boundary Value Problems ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Singularly Perturbed Parabolic Equations

scholarly journals Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions

2006 ◽  
Vol 2006 ◽  
pp. 1-21 ◽  
Author(s):  
Adelaida B. Vasil'eva ◽  
Leonid V. Kalachev
Keyword(s):  
Boundary Layer ◽  
Small Parameter ◽  
Parabolic Equations ◽  
The Other ◽  
Singularly Perturbed ◽  
Stationary States ◽  
Algebraic Equations ◽  
Degenerate Equations ◽  
Singularly Perturbed Parabolic Equations ◽  
Perturbed Periodic

We consider a class of singularly perturbed parabolic equations for which the degenerate equations obtained by setting the small parameter equal to zero are algebraic equations that have several roots. We study boundary layer type solutions that, as time increases, periodically go through two fairly long lasting stages with extremely fast transitions in between. During one of these stages the solution outside the boundary layer is close to one of the roots of the degenerate (reduced) equation, while during the other stage the solution is close to the other root. Such equations may be used as models for bio-switches where the transitions between various stationary states of biological systems are initiated by comparatively slow changes within the systems.

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