Construction de solutions nulles pour des opérateurs non Fuchsiens. (Construction of zero solutions of non-Fuchsian operators) (Q1092221)

This article studies the necessity of the Fuchsian property for the uniqueness of the Cauchy problem. More precisely, it's shown that if the principal part \(P_ m\) of a partial differential operator P is not Fuchsian, uniqueness does not hold in general. Essentially, two cases are considered: The case of real \(C^{\infty}\) phase and the one of analytic phase. In the two situations counterexamples are constructed using perturbations of the operator by a zero order \(C^{\infty}\) flat term.