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Wave propagation in manifolds with corners. (Propagation des ondes dans les variétés à coins.) (French) Zbl 0891.35072

This paper is concerned with the propagation of analytic singularities for the initial boundary value problem for the wave equation in manifolds presenting a wide range of boundary singularities, like conic points, wedges, curved conical points and vertex-wedges (whose model can be described as \(\mathbb{R}_+^p \times \mathbb{R}^q\) near the origin). In a fairly general geometric context the geometry of “bicharacteristic rays” is studied, and results on reflection and propagation of analytic singularities are given. The techniques employed are the microlocalization of the weak formulation of the initial-boundary value problem, use of the F.B.I. transform, and complex scaling as well as Melrose-Sjöstrand method for diffraction.
Reviewer: A.Bove (Bologna)

MSC:

35L05 Wave equation
58J47 Propagation of singularities; initial value problems on manifolds
35S15 Boundary value problems for PDEs with pseudodifferential operators
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
58J45 Hyperbolic equations on manifolds
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References:

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