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Equations Differentielles Operationnelles: Et Problèmes Aux Limites by Jacques Louis Lions

Equations Differentielles Operationnelles: Et Problèmes Aux Limites

by Jacques Louis Lions
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Book cover type: Paperback
  • ISBN13: 9783662237403
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 292
  • Original Price: EUR 60.74
  • Language: German
  • Edition: Softcover Repri
  • Item Weight: 427 grams
  • BISAC Subject(s): Differential Equations / General

Dans un espace de BANACH H soit A(t) une famille d'operateurs non bornes, tE [0, TJ pour fixer les idees. On appelle equation difterentielle operationneUe (lineaire) une equation de la forme A(t)u(t)]u'(t) =f(t), la fonction f Hant donnee continue de [0, TJ dans H, la fonction u Hant une fois continument differentiable dans [0, TJ a valeurs dans H, u(t) appartenant a D(A(t)) (domaine de A(t)) pour chaque tE[O, T]. Les exemples les plus importants sont ceux Oll A(t) est un systeme differentiel, le domaine de A(t) Hant alors fixe par des conditions aux limites. Le probleme de CAUCHY consiste a trouver une solution de (*), verifiant la condition initiale u(O) = u, U donne (dans D(A(O))). o o Mais il est classique que, pour bien des applications, le probleme pose sous la forme precedente impose des conditions trop restrictives a u. Il faut introduire alors la notion de solution faible de ce probleme; il y a un tres grand nombre de telles notions; une classification en est donnee au Chap. 1. Les Chap. IV, V, VII, IX, X donnent diverses con- ditions suffisantes portant sur les A (t) pour que tel ou tel probleme faible admette une solution et une seule; on y Hudie la regularite de ces solutions, et les meilleurs domaines Oll l' on doit prendre les donnees initiales.

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