Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-04-30T11:00:13.739Z Has data issue: false hasContentIssue false
  • English
  • Français

On diffracted wave fronts

Published online by Cambridge University Press:  14 November 2011

Peter Wolfe
Peter Wolfe
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper we study the wave equation, in particular the propagation of discontinuities. Two problems are considered: diffraction of a normally incident plane pulse by a plane screen and diffraction of a spherical wave by the same screen. It is shown that when an incident wave front strikes the edge of the screen a diffracted wave front is produced. The discontinuities are precisely computed in a neighbourhood of the edge for a small time interval after the arrival of the incident wave front and a theorem of Hörmander on the propagation of singularities is used to obtain a globalresult.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 1-2 , 1979 , pp. 35 - 54
Copyright
Copyright © Royal Society of Edinburgh 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Ahluwalia, D. S., Lewis, R. M. and Boersma, J.. Uniform asymptotic theory of diffraction by a screen. SIAM J. Appl. Math. 16 (1968), 783–807.CrossRefGoogle Scholar
2Bloom, C. O. and Kazarinoff, N. D.. Short wave radiation problems in inhomogeneous media: asymptotic solutions. Lecture Notes in Mathematics 522 (Berlin: Springer, 1976).Google Scholar
3Friedlander, F. G.. Sound Pulses (Cambridge Univ. Press, 1958).Google Scholar
4Friedman, A.. Partial Differential Equations (New York: Holt, Rinehart Winston, 1969).Google Scholar
5Hormander, L.. On the existence and regularity of solutions of linear partial differential equations. Enseignement Math. 17 (1971), 99–163.Google Scholar
6Lewis, R. M. and Boersma, J.. Uniform asymptotic theory of edge diffraction. J. Mathematical Phys. 10 (1969), 2291–2305.Google Scholar
7Nirenberg, L.. Lectures on linear partial differential equations. Regional Conference Series in Math. 17 (Providence, R.I.: Amer. Math. Soc., 1973).Google Scholar
8Saltykov, E. G.. The justification of high frequency approximations in the problem of wave diffraction by a plane screen. U.S.S.R. Computational Math. and Math. Phys. 14/1 (1974), 144–155.Google Scholar
9Schwartz, L.. Mathematics for the Physical Sciences (Paris: Hermann, 1966).Google Scholar
10Wilcox, C. H.. Initial-boundary value problems for linear hyperbolic partial differential equationsof second order. Arch. Rational Mech. Anal. 10 (1962), 361–400.Google Scholar
11Wolfe, P.. Diffraction of a scalar wave by a plane screen. SIAM J. Appl. Math. 14 (1966), 577–599.Google Scholar
12Melrose, R.. Microlocal parametrices for diffractive boundary value problems. Duke Math. J. 42 (1975), 605–635.CrossRefGoogle Scholar