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**Diffraction by a convex obstacle.
(Diffraction par un convexe.)**
*(French)*
Zbl 0831.35121

The purpose of the present paper is to derive results regarding the diffraction of waves by an obstacle in adapting a method already used by the first author in the study of the heat equation. It has been conjectured that the decay rate in the shadow area should be in the form \(\exp (- C \omega^{1/3})\) where \(C\) is a constant related to the geometry of the geodesic flow on the boundary of the obstacle.

This result has been already proven for analytic boundaries, and here one considers the case of an obstacle with \(C^\infty\) boundary. The main strategy to establish the basic theorem is the following. (i) The so- called Airy’s inequality, (ii) the estimation of the velocity of propagation on the solving kernels, and (iii) the use of complex deformation on the normal variables on the boundary.

This result has been already proven for analytic boundaries, and here one considers the case of an obstacle with \(C^\infty\) boundary. The main strategy to establish the basic theorem is the following. (i) The so- called Airy’s inequality, (ii) the estimation of the velocity of propagation on the solving kernels, and (iii) the use of complex deformation on the normal variables on the boundary.

Reviewer: G.Jumarie (Montreal)

### MSC:

35P25 | Scattering theory for PDEs |

78A45 | Diffraction, scattering |

35S05 | Pseudodifferential operators as generalizations of partial differential operators |

### Keywords:

obstacle with \(C^ \infty\) boundary; diffraction of waves by an obstacle; decay rate in the shadow area
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\textit{T. Harge} and \textit{G. Lebeau}, Invent. Math. 118, No. 1, 161--196 (1994; Zbl 0831.35121)

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