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Systèmes Lents-Rapides Avec Problèmes Réduits Hamiltoniens by Benbachir-M

Systèmes Lents-Rapides Avec Problèmes Réduits Hamiltoniens

by Benbachir-M
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Book cover type: Paperback
  • ISBN13: 9783838140803
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 64
  • Original Price: GBP 37.0
  • Language: French
  • Edition: N/A
  • Item Weight: 105 grams
  • BISAC Subject(s): General

Les systèmes lents-rapides où systèmes à deux échelles de temps sont des systèmes d'équations différentielles caractérisés par la multiplication de la dérivée d'ordre le plus élevé par un paramètre réel petit. Dans ce travail on s'intéresse aux systèmes d'équations différentielles à deux échelles de temps (systèmes lents-rapides), dont le problème réduit est Hamiltonien avec ou sans paramètre lentement variable, on rappelle les notions de base sur les systèmes lents-rapides ainsi que sur les systèmes Hamiltoniens avec quelques résultats de référence de la littérature. On considère un système lent-rapide dont le système lent est Hamiltonien. Le théorème de Tikhonov nous assure une approximation de l'ordre de 1 des solutions du système lent-rapide considéré. En considérant la région d'oscillations du Hamiltonien et par l'application de la technique de moyennisation, on donne une approximation de l'ordre de 1/ε de l'énergie totale du système et du paramètre, qui sont tous les deux à variation lente. On résout complètement à la main quelques exemples que nous illustrons avec des simulations numériques.

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