B. Messirdi, A. Rahmani, A. Senoussaoui : Problème de Cauchy $C^{\infty }$ pour des systèmes d'équations aux dérivées partielles à caractéristiques multiples de multiplicité paire, p.345-358

Abstract:

The objective of this paper is to establish explicitly with using localization hypothesis, some algebraically conditions of decomposition of a system of partial differential equations with multiple characteristics and pair multiplicity. These conditions are sufficient for the well posedness of the $C^{\infty }$ associated Cauchy problem. The technic of the asymptotically solutions prove that these conditions are also necessary.

Key Words: Problème de Cauchy $C^{\infty }$, hyperbolicité, décomposition d'un opérateur, parametrix.

2000 Mathematics Subject Classification: Primary: 35S30, 35S05,
Secondary: 35P05.

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