Abstract
With the aid of the Kirchhoff approximation, a short-wave asymptote of the scattering of a plane wave is constructed. The fundamental proposition on the geometry of the obstacle consists in its being starlike, which enables one to use estimates derived by Morawets and Ludwig. The constructed asymptote of the scattered wave is used to construct the scattering amplitude and analysis of its peak is used for the forward scattering.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
H. D. Alber, “The highest order singularities of the scattering kernel,” in: Lazarov, Petkov (ed.): Integral Equations and Inverse Problems. Proceedings of a conference held in Varna. Longman, Harlow.
H. D. Alber and R. Leis, Initial boundary value and scattering problems in mathematical physics, in: Hildebrandt S. and Leis R. (eds.): Partial Differential Equations and Calculus of Variations, Lecture Notes in Mathematics 1988, 1357, Springer, Berlin.
H. D. Alber and A. G. Ramm, “Scattering amplitude and algorithm for solving the inverse scattering problem for a class of nonconvex obstacles,” J. Math.Anal. Appl.,117, 570–597 (1986).
P. D. Lax and R. S. Phillips, Scattering Theory, Academic Press, New York (1967).
C. S. Morawetz and D. Ludwig, “An inequality for the reduced wave operator and the justification of geometrical optics,” Commun. Pure Appl. Math.,21, 187–203 (1968).
A. G. Ramm, Scattering by Obstacles, Reidel, Dordrecht (1986).
Additional information
Published in Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova AN SSSR, Vol. 195, pp. 5–13, 1991.
Rights and permissions
About this article
Cite this article
Alber, H.D. Asymptotics of the scattering amplitude in the high-frequency region that are uniform in L2 . J Math Sci 62, 3053–3058 (1992). https://doi.org/10.1007/BF01095675
Issue Date:
DOI: https://doi.org/10.1007/BF01095675