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Stability with Respect to Perturbations

  • P. Constantin
  • C. Foias
  • B. Nicolaenko
  • R. Teman
Part of the Applied Mathematical Sciences book series (AMS, volume 70)

Abstract

We prove in the chapter the stability of the inertial manifolds constructed before with respect to perturbations. Three types of perturbations will be explicitly considered here: perturbations of the operators corresponding to a Galerkin approximity of the problem, perturbation of the viscosity parameter v, and perturbation of the right-hand side f (see(4.1)). Although we restrict ourselves to these three perturbations for the sake of simplicity, we believe that our perturbation results apply to more general situations.

Keywords

General Situation Lipschitz Constant Isoperimetric Inequality Galerkin Approximation Integral Manifold 
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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • P. Constantin
    • 1
  • C. Foias
    • 2
  • B. Nicolaenko
    • 3
  • R. Teman
    • 4
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA
  3. 3.Center for Nonlinear StudiesLos Alamos National LaboratoryLos AlamosUSA
  4. 4.Department de MathematiquesUniversité de Paris-SudOrsayFrance

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