On the stability and domain of attraction of asymptotically nonsmooth stationary solutions to a singularly perturbed parabolic equation

2006 ◽  
Vol 46 (3) ◽  
pp. 413-424 ◽  
Author(s):  
V. F. Butuzov
Keyword(s):  
Parabolic Equation ◽  
Domain Of Attraction ◽  
Stationary Solutions ◽  
Singularly Perturbed ◽  
Singularly Perturbed Parabolic Equation ◽  
The Stability

Stable Transition Layers to Singularly Perturbed Spatially Inhomogeneous Allen-Cahn Equation

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Arnaldo Simal do Nascimento ◽  
Maicon Sônego
Keyword(s):  
Parabolic Equation ◽  
Geometric Structure ◽  
Stationary Solutions ◽  
Singularly Perturbed ◽  
Transition Layers ◽  
Cahn Equation ◽  
Spatially Inhomogeneous ◽  
Singularly Perturbed Parabolic Equation ◽  
Γ Convergence

AbstractWe use the variational concept of Γ-convergence to prove existence, stability and exhibit the geometric structure of four families of stationary solutions to the singularly perturbed parabolic equation u

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