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Zbl 0648.35087
Diomeda, Lorenza; Lisena, Benedetta
Propagation, reflection and refraction of singularities for a hyperbolic transmission problem in two adjacent angular regions. (English)
[J] Rend. Semin. Mat. Univ. Padova 78, 1-26 (1987). ISSN 0041-8994

The main purpose of this paper is to study propagation and reflection of singularities of the solution of a transmission problem for the wave equation with different sound speeds in two adjacent angular regions which have amplitude $\pi$ /2. The initial and boundary data are opportune distributions with compact support. The classic method of images and the theory of pseudodifferential operators are used to find an explicit potential representation of a solution of the considered transmission problem. It is shown that the singularities of such solution travel along bicharacteristic lines coming out from points of the wave front set of boundary and initial data. If the singularities have origin from boundary data there are reflection and refraction phenomena on the faces of the angular regions, according to the geometric optics. If the singularities arise from the initial data reflection phenomena on the edge also occur.
[L.Diomeda]
MSC 2000:
*35S15 Boundary value problems for pseudodifferential operators
35B40 Asymptotic behavior of solutions of PDE
35L20 Second order hyperbolic equations, boundary value problems
78A05 Geometric optics
35A20 Analytic methods (PDE)

Keywords: propagation; reflection; singularities; transmission problem; wave equation; different sound speeds; explicit potential representation; bicharacteristic lines; wave front set; refraction; angular regions; geometric optics

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