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On présente une famille de problèmes mixtes hyperboliques linéaires bien-posés au sens de Hadamard. La nouveauté consiste à autoriser une perte de régularité entre les termes source et la solution. On montre ainsi que la condition de Lopatinskii faible est suffisante pour obtenir le caractère bien-posé des problèmes mixtes hyperboliques linéaires.
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