A family of approximate inertial manifolds for a Van der Pol/FitzHugh–Nagumo perturbation problem

2011 ◽  
Vol 88 (7) ◽  
pp. 1443-1470
Author(s):  
Joseph L. Shomberg ◽  
Cristina Nartea
Keyword(s):  
Inertial Manifolds ◽  
Van Der Pol ◽  
Perturbation Problem ◽  
Approximate Inertial Manifolds

Efficient methods using high accuracy approximate inertial manifolds

2001 ◽  
Vol 87 (3) ◽  
pp. 523-554 ◽  
Author(s):  
Julia Novo ◽  
Edriss S. Titi ◽  
Shannon Wynne
Keyword(s):  
High Accuracy ◽  
Inertial Manifolds ◽  
Approximate Inertial Manifolds

scholarly journals Reduction of dimension of approximate intertial manifolds by symmetry

1999 ◽  
Vol 60 (2) ◽  
pp. 319-330
Author(s):  
Anibal Rodriguez-Bernal ◽  
Bixiang Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Inertial Manifolds ◽  
Inertial Manifold ◽  
Partial Differential ◽  
Approximate Inertial Manifold ◽  
Approximate Inertial Manifolds ◽  
The Relationship

In this paper, we study approximate inertial manifolds for nonlinear evolution partial differential equations which possess symmetry. The relationship between symmetry and dimensions of approximate inertial manifolds is established. We demonstrate that symmetry can reduce the dimensions of an approximate inertial manifold. Applications for concrete evolution equations are given.

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