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On the solutions of the wave equation with discontinuous derivatives

Published online by Cambridge University Press:  24 October 2008

F. G. Friedlander
F. G. Friedlander
Affiliation:
Trinity CollegeCambridge
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Extract

The differential equation of wave propagation is

where u is a variable describing the state of a medium, x, y, z are rectangular coordinates, and r is the time (the time scale is assumed to be such that waves are propagated with unit velocity).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 4 , November 1942 , pp. 378 - 382
Copyright
Copyright © Cambridge Philosophical Society 1942

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References

REFERENCES

(1)Love, . Wave motions with discontinuities at wave-fronts. Proc. London. Math. Soc. (2) 1 (1903), 37.Google Scholar
Hilbert-Courant, . Methoden der Mathematischen Physik, 2 (Berlin, 1937), 356.CrossRefGoogle Scholar
(2)Hilbert-Courant, . Methoden der Mathematischen Physik, 2 (Berlin, 1937), 364.CrossRefGoogle Scholar
(3)See, for example, Lamp, , Hydrodynamics (6th ed.Cambridge, 1932), p. 494.Google Scholar
(4)Friedlander, . Note on a limit related to the curvatures of two surfaces. Proc. Cambridge Phil. Soc. 38 (1942), 399.CrossRefGoogle Scholar
(5)See, for example, Jeffreys, , Operational Methods in Mathematical Physics (Cambridge, 1931), p. 80.Google Scholar
(6)Frietlander, . The reflexion of sound pulses by convex parabolic reflectors; Proc. Cambridge Phil. Soc. 37 (1941), 149.Google Scholar