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Résolution de l''équation Du Transport Sous Contraintes by Picq-M

Résolution de l''équation Du Transport Sous Contraintes

by Picq-M
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Book cover type: Paperback
  • ISBN13: 9786131508127
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 172
  • Original Price: GBP 49.0
  • Language: French
  • Edition: N/A
  • Item Weight: 259 grams
  • BISAC Subject(s): Reference

Ce travail est consacré à l'étude de l'équation du transport sous contraintes convexes ou non convexes. Dans le cas convexe les résultats connus utilisant la théorie des opérateurs maximaux monotones sont urilisés. Lorsque les contraintes ne sont pas convexes la méthode des caractéristiques sous forme autonome pour un flot temps-espace est mise en oeuvre, en particulier une démonstration détaillée du théorème de remplissage d'un ouvert lipschitzien par les caractéristiques est donnée. Une approche géométrique des contraintes utilisant les cônes contingents et le théorème de Nagumo est alors possible. Des exemples simples illustrent les règles difficiles du calcul des cônes contingents. L'introduction d'une notion de contingence pour un champ de vecteurs continu, caractérisable en termes de contingence extérieure et qui s'applique à tout image réciproque d'un convexe permet une véritable généralisation des résultats obtenus dans le cas convexe. Des méthodes numériques adaptées sont présentées. L'intérèt de cette approche a été confirmée dans des travaux publiés ultérieurement et dédiés à l'analyse de séquences d'images en imagerie médicale dynamique cardiaque.

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