The connection between stability of equilibrium and propagation of small disturbances through a general elastic medium has been stated, since 1903, by J. Hadamard. However a doubtful element in the original proof of the theorem was pointed out by P. Duhem. A more elaborated proof, which seems to be satisfactory even in a more general hypothesis, has been later proposed by the author of this report. That proof is reconsidered in this article which deals, in a general context, with the relations between wave propagation and linear stability. A new elegant proof of Hadamard's theorem, recently proposed by G. Fichera, is briefly reported at the end of the article.
RI~SUMI~
Les liens entre la stabilit6 de l'6quilibre et la propagation des ondes dans un milieu ~lastiq ue ont 6t6 codifi6s d6s 1903, par J. Hadamard. La d6monstration origiuaire du th6or~me pr6sente toutefois un point douteux, mis en 6vidence par P. Duhem. Une d6monstration plus 61abor6e, qui parait math6matiquement corr+cte m~me en des conditions physiques plus gdn6rates, a 6t6 propos6e plus tard par l'auteur de cet expos6. Cette d6monstration est reprise dans l'article suivant, qui envisage dans un contexte g6n6ral les relations entre la propagation des ondes et la stabilit6 lin6aire. Une nouvelle et 616gante d6monstration du th6or6me de Hadamard, propos6e r6cemment par G. Fichera, est r6sum6e b. la fin de l'article.