Inertial Manifolds for Partial Differential Evolution Equations under Time- Discretization: Existence, Convergence, and Applications
نویسنده
چکیده
Dans ce travail nous ttudions l’existence et la convergence de variites inertielles pour la discretisation en temps d’equations d’evolution. Nous montrons que pour des pas de temps petits, et sous une condition qui assure l’existence de varietts inertielles exactes (condition d&cart spectral), le probleme disc&i& posdde une varitti: inertielle de mCme dimension. Nous montrons la convergence de la variett approchte vers la variete exacte dans un sens fort et avec estimation d’erreur. Nos applications comprennent des equations non dissipatives, elles ne sont pas limit&es au cas purement parabolique. C’est ainsi que nous considerons des equations d’amplitude du type Ginzburg-Landau et des perturbations dissipatives des equations de Kortewegde Vries.
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