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Propagation des singularités pour des équations hyperboliques à caractéristiques de multiplicité au plus double et singularités Masloviennes. II. (Propagation of singularities for hyperbolic equations with characteristic of multiplicity greater than two and Maslov singularities. II). (French) Zbl 0592.58053
[For Part I see the first author, Am. J. Math. 104, 227-285 (1982; Zbl 0506.35067).]
The authors construct explicit solutions to hyperbolic equations with at most double characteristics; the equations are noneffectively hyperbolic according to the classification of V. Ya. Ivrij and V. Petkov [Usp. Mat. Nauk 29, No.5(179), 3-70 (1974; Zbl 0312.35049)] and L. Hörmander [J. Anal. Math. 32, 118-196 (1977; Zbl 0367.35054)]. The double characteristics N form a noninvolutive \(C^{\infty}\) manifold. They study the case \(p=D^ 2_ 0-A(x,D_ x)\), where A is a classical pseudodifferential operator with nonnegative principal symbol which vanishes exactly of order two on a symplectic submanifold of \(T^*X\setminus O\). They suppose that a positivity condition on the subprincipal symbol and on the fundamental matrix is satisfied in order to have a well-posed Cauchy problem. They used first author’s method from part I. The explicit solution is used to study the propagation of singularities.
Reviewer: R.Vaillancourt

MSC:
58J47 Propagation of singularities; initial value problems on manifolds
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