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Inverse scattering problem for the Maxwell equations outside moving body. (English) Zbl 0675.35066

The paper presents results obtained in the spirit of the work of Cooper and Strauss on scattering of acoustic waves by moving obstacles. Here electromagnetic waves in vacuum are considered. The main focus is on transferring the results on the leading singularity of the scattering kernel to this situation. Crucial is the use of a suitable “elliptization” of Maxwell’s equations in order to facilitate the construction of a micro-local parametrix. After obtaining a suitably adapted translation representation the author develops a representation of the scattering kernel. Based on this and the construction of a parametrix the leading singularity of the scattering kernel can be isolated. As a corollary the possibility to recover the convex hull of the obstacle from the back-scattering data is confirmed.
Reviewer: R.Picard

MSC:

35P25 Scattering theory for PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
78A25 Electromagnetic theory (general)
47A40 Scattering theory of linear operators
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References:

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